Maybe the simple reason is that for the husband to have stability (and a man will take care of somthing/someone that is his, that can not be taken away much better then somthing that can leave)
Marrige is not what it seems now (a new idea maybe less then 100 years) to the western world
In short, the answer is because this is what G-d Almighty told us.
Marriage is an old thing.
It was given to us by G-d, and it starts by the husband offering it to his wife and she willfully accepts (if she was forced it is invalid) and it ends when he gives something to his wife and she accepts.
See Mishneh Torah» Sefer Nashim » Gerushin - Chapter One
What are the sources that indicate that these ten requirements stem from Scripture itself? [They are derived from Deuteronomy 24:1, which] states: "And if it comes to pass that she does not find favor in his eyes, and he will write a bill of divorce for her, place it in her hand and send her from his home.".
"If... she does not find favor in his eyes" - this indicates that he divorces her only on his own initiative. If a woman is divorced against her husband's will, the divorce is invalid. A woman may, however, be divorced either voluntarily or against her will. (Biblically speaking)
"And he will write" - this teaches that a woman can be divorced only by means of a written document.
"For her" - that it should be written for her sake.
"A bill of divorce" - i.e., a deed that severs the relationship between [the husband and his wife], without leaving him any jurisdiction over her. If [the relationship] between them is not entirely severed, the divorce is not effective, as will be explained...
Sorry, I will be very frank.
The man take a wife for himself (and no one else can use her).
He can let her free.
Similarly, in the Russian language until today the man gets married and the woman does not (she goes for the husband)
An inexact analogy will be (the gemoro menachot 43b on bottom,
And is not that (a slave) the same as a woman? ( rashi explains this question either 1 a woman is a maidservant to her husband is as a slave to his master or 2 For with regard to the performance of precepts a woman and a slave are on the same footing;)(answer:) A slave is more contemptible.
(R' Moshe Feinstein sais that if it was not rashi he would say it is wrong, since when looking at all of the wife's rights, it is the husband who is the slave to his wife! (biblically the husband only has one right over his wife and that is to use her (intimacy))).
a slave, a slave belonging to a jew has a lot of rights but can not let himself free, only the master can let him free,
G-d almighty took/chose the Jews, the Jews exepted now they can not turn away
The condition that only he can divorce her was one of the conditions that she agreed to him to marry her.
Why do you think that the woman should have the right to devorce?
@vaxquis below brings a good point "since a woman brings the child and takes care of raising it, the man has to take care of her. Since it's he who is the caretaker and she is the one who is taken care of, she can't apply for divorce the same way a tree can't uproot itself. She can leave, she can kill the husband, she can do a lot of things, she can act - but should that imply it would be according to the G-d's law? If you're a true Jew, you respect the tradition. If you don't want to respect that tradition, nobody forces you to be a Jew"
@DoubleAA probably wants me to add some of the obligations of a husband to his wife
Similarly, our Sages commanded that man honor his wife more than his own person, and love her as he loves his own person. If he has financial resources, he should offer her benefits in accordance with his resources. He should not cast a superfluous measure of fear over her. He should talk with her gently, being neither sad nor angry.