Matthew Pocket, the father of Herbert, has been hired to be the tutor of the aspiring gentleman, Pip.  Truly a gentleman himself, Matthew Pocket is a man of integrity who has refused to be a sycophant as have the other Pockets who attend Miss Havisham on her birthday as she walks around the decaying cake.

When Pip comes to the home of the Pockets, however, he encounters an extremely dysfunctional family in which Mr. Pocket is totally ineffective.  For, he has no control over his frivolous wife who is oblivious to the actions of her small children as she sits absorbed in a book of English titles. In Chapter XXII, Pip is introduced by Herbert to Mrs. Pocket and he observes,

I found, now I had leisure to count them, that there were no fewer than six little Pockets present, in various stages of tumbling up. I had scarcely arrived at the total when a seventh was heard, as in the region of air, wailing dolefully....

Thus I made the second discovery on that first occasion, that the nurture of the little Pockets consisted of alternately tumbling up and lying down.

Under these circumstances, when Flopson and Millers had got the children into the house, like a little flock of sheep, and Mr. Pocket came out of it to make my acquaintance, I was not much surprised to find that Mr. Pocket was a gentleman with a rather perplexed expression of face, and with his very gray hair disordered on his head, as if he didn't quite see his way to putting anything straight.

Pip soon learns that Mrs. Pocket is the daughter of a man who was a "quite accidental deceased knight," whose father should have received a title; thus, Mrs. Pocket searches through books of titles to find that of her ancestor. On the other hand, Mr. Pocket has no title; he watches helplessly as the children tumble over their mother's leg while she obliviously continues her reading.

Still, Mrs. Pocket was in general the object of a queer sort of respectful pity, because she had not married a title; while Mr. Pocket was the object of a queer sort of forgiving reproach, because he had never got one.

After Pip is introduced to the other students, Bentley Drummle and Startop, he observes Mr. Pocket's household further. He notices that it is the servants who raise the children as neither parent controls them.  However, the servants take it upon themselves to physically discipline the children and also to partake of the best food that the Pockets have.  When "the page" enters and tells the Pockets that the cook has mislaid the beef, a frustrated Mr. Pocket 

... laid down the carving knife and fork—being engaged in carving at the moment—put his two hands into his disturbed hair, and appeared to make an extraordinary effort to lift himself up by it. When he had done this, and had not lifted himself up at all, he quietly went on with what he was about.

Although a man of good heart and manners, Matthew Pocket has no control over his household.

Hired to be the tutor of Pip in his "great expectations," Mr. Matthew Pocket is an erudite gentlemen with only one fault:  he cannot handle his domestic affairs. Ironically, in theory, Mr. Pocket is very competent in this area, but in reality, he is incapable of maintaining any order in his home.

Mr. Pocket was out lecturing; for he was a most delightful lecturer on domestic economy, and his treatises on the management of children and servants were considered the very best text-books on those themes.

In Chapter XXII, for instance, Mrs. Pocket, who is quite helpless, spends her time reading about titles; as she buries herself in her book, her children fall about her, tumbling over Mrs. Pocket's footstool. The maid Flopson finds herself retrieving the children from under her feet or rescuing them from choking on nutcrackers.

“Good God!” cried Mr. Pocket, in an outbreak of desolate desperation. “Are infants to be nutcrackered into their tombs, and is nobody to save them?”

This contrast in Mr. Pocket's persona as a man of letters and his frustrated and inept persona as a husband provides comic relief in this tale of the trials and tribulations of maturing. In addition, there is a suggestion that Pip may not become any more productive than the Pockets. 

Matthew Pocket's chief fault is that he made the common mistake of marrying while he was too young and before he had decided on a career. He didn't know whether to go into the law or the church, and consequently did neither. Dickens describes them both as having married "in the first bloom of youth." Mrs. Pocket is described as having grown up

. . . highly ornamental, but perfeftly helpless and useless.

She is very good at having babies, but no good whatsoever in taking care of them. The household is chaotic. Mr. Pocket has his hands full trying to make a living without having any specialized training for a profession. He is constantly frustrated by the disorganized state of his household, which the servants run to please themselves. He is in the habit of grasping his hair with both hands and seemingly trying to pull himself up.

He laid down the carving knife and fork--being engaged in carving at the moment--put his two hands into his disturbed hair, and appeared to make an extraordinary effort to lift himself up by it.

Matthew Pocket is an intelligent and likeable man, but thoroughly disorganized himself anf married to a giddy young woman who is even more so. He makes his living in whatever way he can with the education he has received at Harrow and Cambridge before getting married too soon and finding himself saddled witth a childish and incompeent wife and growing family. Part of his living comes from tutoring young gentlemen. He also, paradoxically, writes books and gives lectures on such subjects as domestic management and the care and raising of children.

Why is Matthew Pocket especially suitable to educate Pip? Precisely because Pip's secret benefactor does not want him educated for any profession or trade, and Pocket himself was not educated for any profession or trade. He will teach Pip how to have the appearance of a gentleman and to be able to talk the chit-chat that characterizes genteel society. Pip thinks his real purpose in life is just to be a husband to the beautiful Estella, and he believes that is what Miss Havisham, whom he has always taken to be his benefactress, expects of him. The unknown benefactor (Magwitch) plans to leave him plenty of money and only wants him to turn into his idea of a "gentleman," which is what Pip actually becomes. Poor Magwitch, like members of the ignorant lower classes in general, admires gentlemen and ladies, with their fine clothes and manners, without understanding that most of them are parasites living off the labor of people like Magwitch himself.

After two or three days, when I had established myself in my room and had gone backwards and forwards to London several times, and had ordered all I wanted of my tradesmen, Mr. Pocket and I had a long talk together. He knew more of my intended career than I knew myself, for he referred to his having been told by Mr. Jaggers that I was not designed for any profession, and that I should be well enough educated for my destiny if I could "hold my own" with the average of young men in prosperous circumstances. I acquiesced, of course, knowing nothing to the contrary.

When Magwitch returns illegally to England and meets Pip in his rooms, he is delighted with the gentleman he has made with his hard toil and spartan existence in Australia. Pip is actually quite spoiled and useless, not capable of earning his own living, and contemptuous of the working classes. He lives a life of leisure and dissipation. He has become a fop.