I don't think coming up with an agreed-upon answer to this question is a prerequisite to evangelical/Mormon dialog, but it is nonetheless worth addressing. My short answer is that my evangelical DNA in Christ has woven strands of evangelism, mission, neighborly love, healthy human community, curiosity, and a desire to be accurate in my engagement and representation of Mormon views when I portray them elsewhere.

I am not one for denigrating the stands of evangelism and mission --- they are the most significant for me. I want people to believe as I do and to be evangelical Christians.

To clear up the many, many misconceptions Evangelicals have about the LDS Church and its teachings and practices.

Recently I've been in a dialog group with some people from CES. When I joined I was asking myself this very question? Here are some reasons why I did initially, and some I have adopted along the way.
1. to be a good neighbor
2. to break down stereotypes and caricatures of others toward me and of me toward them
3. to help me better assess what contemporary Mormonism is saying about important issues
4. to make sure that when I speak or write about Mormonism, that I am accurate and fair
5. to model the grace of God in my attitudes and actions
6. to correct misconceptions they might have about evangelical beliefs and practices
7. to encourage my friends to consider what the historic evangelical gospel has to offer to LDS