JOEL - Actually we are not supposed to "try and convert people". The Holy Ghost does that. We are only commanded by God to present the Gospel to people and give them the chance to obtain eternal life. The following scriptures explains this.

D&C 88:81
"Behold, I sent you out to testify and warn the people, and it becometh every man who hath been warned to warn his neighbor."

Matthew 28:19
"Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:"

D&C 18:15-16
15. "And if it so be that you should labor all your days in crying repentance unto this people, and bring, save it be one soul unto me, how great shall be your joy with him in the kingdom of my Father!
16. And now, if your joy will be great with one soul that you have brought unto me into the kingdom of my Father, how great will be your joy if you should bring many souls unto me!"

D&C 4:4
"For behold the field is white already to harvest; and lo, he that thrusteth in his sickle with his might, the same layeth up in store that he perisheth not, but bringeth salvation to his soul;"

We do it because God has told us to do it. We also do it because all the people of the earth are our spiritual brothers and sisters, who we love. Because we love them, we care about their eternal future and happiness and want to help them in any way we can to obtain eternal life with God. We also do it for the joy it will bring to us and for our own salvation.