Why is Egeus angry with Hermia in act 1, scene 1 of A Midsummer Night's Dream?

Egeus is angry with his daughter Hermia because she is disobeying his will for her to marry Demetrius. Because Hermia is disobeying him, he is petitioning Theseus to sentence her with Athens' "ancient privilege," meaning the right to either kill her or send her off to a convent (I.i.42). However, it should be noted that while sending her to a convent is an option, Egeus is asking permission to "dispose of her" either through marriage to Demetrius or through death, rather than sending her to a convent (43-46).

It should also be noted that Shakespeare seems to be questioning Egeus's decision to have Hermia marry Demetrius in stead of Lysander. Egeus accuses Lysander of seducing his daughter and "betwitching" her through poems, "love-tokens," and singing insincere love songs beneath her window by the moonlight (28-32). In short, he is accusing Lysander of not truly loving his daughter but merely trying to seduce her. However, Shakespeare also points out that the sincerity of Demetrius's love is actually what Egeus should be suspicious of. Lysander argues that Demetrius is actually the insincere one because he has already seduced Helena and won her heart and "soul" to the point that she "dotes" upon Demetrius, "Devotedly dotes, dotes in idolatry" (110-111). Theseuss even confirms Lysander's accusations of Demetrius by saying that he has heard the same thing (113). We actually learn towards the end of the play that Demetrius not only seduced Helena and made vows of love, but he was actually engaged to her.  Hence, Shakespeare is pointing out that Demetrius's character is questionable, showing us the questionability of Egeus's decision to want him to marry Hermia.

Aside from Demetrius's character being questionable, we also learn from Lysander in this scene that he is equal to Demetrius in social status and possibly even wealthier, as we see in his lines:

I am, my lord, as well derived as he,
As well possess'd; my love is more than his;
My fortunes every way as fairly rank'd,
If not with vantage, as Demetrius'. (101-104)

Hence, Shakespeare is showing us that there is no rationality behind Egeus's decision to want Demetrius to marry his daughter instead of Lysander and no rational reason to have her killed should she disobey. Egeus's anger and his decisions help portray Shakespeare's theme of questioning the rationality of man.

Is Egeus justified in being angry with his daughter in Act 1, Scene 1 of A Midsummer Night's Dream?

The answer to this question is wholly dependent on perspective. In the eyes of the law, Hermia is Egeus' daughter, therefore she is his property until he hands her off to a husband. As such, he is allowed to do with her as he wishes and she is not to have any say in the matter. However, from a modern perspective, we view this as repressive and controlling behavior because, as an American society, we do not accept the concept of arranged marriages. It is important, however, to acknowledge that some cultures do still view arranged marriages as the norm, so again the potential justification for his anger is largely dependent on the reader.

Hermia has defied her father. We do accept that children should not defy their parents as long as their parents requests or demands are reasonable. The question, then, is is Egeus' demand that Hermia marry Demetrius reasonable?

This is a matter of perspective, but it can also be argued that Shakespeare, given his resolution in this work as well as his tragic outcome in Romeo and Juliet, had his own opinions about parental involvement in their children's relationships. From the writer's perspective, therefore, it is arguable that his anger is not justified.

Why is Egeus angry with his daughter in A Midsummer Night's Dream?

Egeus is a nobleman of Athens who becomes angry with his daughter, Hermia, because she is not obedient to him. While his wish is that his daughter marry Demetrius—who, despite having once loved Helena, does truly love Hermia—Hermia does not love Demetrius. Instead, she is in love with Lysander. In his anger, Egeus marches into the court of Theseus, Duke of Athens, and requests that his will be obeyed or the "ancient privilege of Athens" be evoked against his daughter:

As she is mine, I may dispose of her;
Which shall be either to this gentleman [Demetrius]
Or to her death, according to our law
Immediately provided in that case. (1.1.42-45)

When Hermia responds to this demand by saying that she wishes her father "looked but with my eyes," she also declares that she will not yield to her father's wish—"My soul consents not to give sovereignty" (1.1.84). Nevertheless, she is told by the duke that she must comply with her father's desires or she will suffer the consequences of death or of having to "adjure/Forever the society of men" (1.1.67-68) by becoming a nun.

Hoping to escape the patriarchal matchmaking of Egeus, Hermia and Lysander decide to elope. Before running off, Hermia informs her friend Helena what she is about to do. Helena follows them, desiring to regain Lysander, who once loved her. A number of complications result as the human world conflicts with the fairy world in the woods, but eventually all is made right.

At the end of the play, Egeus learns that Lysander and Hermia tried to flee Athens. Irate, he insists the couples should be punished. However, Theseus tells Egeus,

I will overbear your will,
For in the temple, by and by with us,
These couples shall eternally be knit [married].....
Away with us to Athens....
We'll hold a feast in great solemnity....(5.1.170-174)

Later, Theseus degrees that Demetrius and Helena are finally married, as are Lysander and Hermia.