Why has Egeus brought his daughter and her two suitors to Theseus in A Midsummer Night's Dream?

Egeus wants Theseus to force his daughter to marry Demetrius, the man of his choice.

Egeus has a problem.  His daughter does not want to marry the man he chose for her to marry.  Instead, she fell in love with someone else.  He goes to the king of Athens, Theseus, and asks him to intercede.

Full of vexation come I, with complaintAgainst my child, my daughter Hermia.Stand forth, Demetrius. My noble lord,This...

Egeus wants Theseus to force his daughter to marry Demetrius, the man of his choice.

Egeus has a problem.  His daughter does not want to marry the man he chose for her to marry.  Instead, she fell in love with someone else.  He goes to the king of Athens, Theseus, and asks him to intercede.

Full of vexation come I, with complaint
Against my child, my daughter Hermia.
Stand forth, Demetrius. My noble lord,
This man hath my consent to marry her.
Stand forth, Lysander: and my gracious duke,
This man hath bewitch'd the bosom of my child… (Act 1, Scene 1)

In Athens, a girl is basically the property of her father.  He will choose her husband, and she does not have a choice in the matter.  In this case, both Lysander and Demetrius are in love with Hermia but only one has his blessing.

Egeus tells Hermia that her father “should be as a god” to her, and his will is all that matters.  He gives her no good choices.  She can marry Demetrius, she can become a nun, or she can die.  As long as her father wants her to marry Demetrius, this is the situation.

Hermia reacts as most young girls would.  She insists that Lysander is “worthy” and begs for Theseus to pardon her.  Despite the dire consequences, she is stubborn.

So will I grow, so live, so die, my lord,
Ere I will my virgin patent up
Unto his lordship, whose unwished yoke
My soul consents not to give sovereignty. (Act 1, Scene 1)

Theseus urges her to take some time to think it over.  What she does do is try to elope with Lysander.  Things get extra complicated when she tells her friend Helena what is going on.  You see, Helena is in love with Demetrius!

As the pairs of lovers head into the forest, mayhem and hilarity ensue.  There are fairies and actors, and plenty of young hormones at work.  This is one of those instances where Egeus would have been better off just listening to his daughter.  In the end, he relents, and she is able to marry her love.  He would rather have his daughter with her choice than not have her at all.