Why does Doctor Faustus choose necromancy?

At the beginning of the play, the Chorus informs the audience that Faustus is "glutted ... with learning's golden gifts" and that he "surfeits upon cursed necromancy." In other words, Faustus has become a very learned man, mastering the intellectual pursuits that would have been seen as legitimate for a scholar in his time. Yet he is unsatisfied with all of this knowledge, because it does not confer upon him the power that he craves. He complains that logic, rhetoric, "disputation," and other conventional intellectual pursuits seem to have no tangible benefits to those who master them. So he turns to necromancy, which in this context basically means "black magic."

In short, Faustus sees magic as the path to power, riches, and fame, and he is willing to bargain his eternal soul in order to master it. He is unsatisfied with what his worldly wisdom has brought him and, rather than reflecting on the limits of knowledge, he wants more. He is entreated early in the play to turn his attentions to the study of Scripture as the path to true wisdom, but he chooses the easier path, one of pleasure and power.

In the beginning, the Chorus compares Faustus to Icarus, the figure in Greek mythology whose homemade wings melted when he flew too close to the sun. His decision to turn to "necromancy" was one born of excessive arrogance and hubris, and it brought about his downfall.

Why does Faustus prefer necromancy over philosophy in Doctor Faustus?

Dr. Faustus prefers necromancy over philosophical inquiry for the simple reason that it gives him access to power, which is what he wants more than anything in the whole world. Besides, philosophical inquiry requires a good deal of thought, study, and effort, and Faustus has pretty much had enough of all that.

Truth be told, he's been getting rather bored lately with the pursuit of knowledge, which is becoming an increasingly fruitless exercise. What he wants is instant knowledge, knowledge he doesn't have to work for, knowledge that is handed to him on a silver platter. With this knowledge—the knowledge provided by necromancy—he wants to exercise power over others, to astonish and dazzle them, to be renowned the world over as a great magician. No amount of hard philosophical labor could ever possibly bring Faustus such power and fame.

Why wasn't Faustus satisfied after leaving Christianity and taking up necromancy?

The first indicator that Faustus will not be satisfied after mastering magic and making a compact with the Devil is Mephistophilis' response to him when required to fulfill Faustus' commands, what ever they may be, including releasing the moon's orbit or releasing the ocean's boundaries:

FAUST. To do whatever Faustus shall command,
Be it to make the moon drop from her sphere,
Or the ocean to overwhelm the world.

Mephisto answers a very clear no, saying that he takes his orders from Lucifer and no one else:

MEPHIST. I am a servant to great Lucifer,
And may not follow thee without his leave:
No more than he commands must we perform.

Another indication that Faustus will be dissatisfied is the conversation he and Mephisto have later about specific knowledge Faustus wants. You'll recall from Faustus' introductory speech that he wants to control all the elements of the world and have dominion over all. In view of this, he asks Mephisto who made the world. Mephisto says he won't tell. Soon Lucifer himself comes to remind Faustus that he is damned and that his knowledge will encompass what Lucifer wants him to know; this is a definite departure from Faustus' original plans.

FAUSTUS. ...  Tell me who made the world?
MEPHIST. I will not.
FAUSTUS. Sweet Mephistophilis, tell me.
MEPHIST. Move me not, for I will not tell thee.
FAUSTUS. Villain, have I not bound thee to tell me any thing?

This conversation with Mephisto drives Faustus to call upon the name of Christ to "Seek to save distressed Faustus' soul!" which leads in to a final example showing Faustus' dissatisfaction. At the end of the play, the Old Man and the Scholars come to help Faustus turn at the last minute and express repentance and seek salvation from God for compacting with Lucifer. Yet, two things prevent Faustus from doing this: (1) he asks the Old Man how to do this but has no chance to hear the answer; (2) he fears the physical pain Mephistophilis and Lucifer have promised him if he tries to call upon God. His agonies in the last scene clearly show his dissatisfaction:

O, I'll leap up to my God!—Who pulls me down?—
See, see, where Christ's blood streams in the firmament!
One drop would save my soul, half a drop:  ah, my Christ!—
Ah, rend not my heart for naming of my Christ!
[...]
No, Faustus, curse thyself, curse Lucifer
That hath depriv'd thee of the joys of heaven.