There is obviously a lot of confusion in your mind on this, but try making a couple of simple assumptions which might help you understand.
Suppose -- just suppose for the purpose of the argument -- that you became convinced that the God of the Universe had somehow imparted His essence to earth in the form of a very special human who could and did, in turn, disclose the very essence of human life. Further presume that you became convinced that this Man and His sayings and doings were accurately recorded in a book which had been accurately preserved over a great deal of time.
Naturally, you would think that, since this Person had opened the best of life to you, the very nicest, kindest, most generous thing you could do would be to share it with others struggling on in the darkness, bumping into things for lack of that Person in their lives.
No surprise. Now, can people be wrong about the details, but you can't really blame people for wanting to tell you or your children about the most important Person in history -- assuming of course that the Bible is true.
So IF it is true, it is quite reasonable to "try to convert" you as you put it. IF it is not, they are simply being arbitrary.
That is an excellent question, and one more people should ask, including those who believe they need or ought to convert the world.
I believe you probably understand at least part of the answer already, and could give it yourself. There is a little bit of the evangelist in most of us. If we believe something strongly, there is an urge to convince others that have not yet discovered this truth, whatever it is, that means so much to us. This kind of evangelism is pretty much based on good will and a desire to share what we believe is true and good.
A more ardent and not always so innocent form of evangelism comes from a belief that one is mandated by their God or their religion to convert others, to "save their souls," from something. Often this kind of evangelism is mixed with a militant fervor, with either an implicit or explicit conviction that one is part of a Holly mission or plan that depends on one's doing their part. So long as this kind of militant evangelism is not combined with a belief that one is justified in using force, though it may be extremely annoying, it is not dangerous.
Finally, there is the rare form of religious conviction that one is mandated by God (or Allah) to convert others, or at least bring them under the control of, "God's law," and that they are justified in using force, or terrorism, or outright deception (if the opportunity for force and terrorism has not yet arrived) to fullfill their mission. This form of "evenagelism" has cropped up in many religions, but always as an anomoly and perversion of the main body of the religion. In the Muslim religion, it has historically been the dominate form, and in terms of raw numbers, it is the dominate form today.
Hank