That's a great question. And even many converts can't quite pinpoint their own reasons for being willing to join a group so hated and persecuted. It always seems to be a mixture of so many feelings, ideas, beliefs, and experiences. Unfortunately, no matter how organic it seemed to you, random strangers and your beit din are going to want some kind of an answer rather than a confused look or "It felt right." Let's discuss what might be some of those component parts of your motivations:
Philosophy: A feeling that the Jewish approach to G-d, the world, and our behavior is right. It's just downright reasonable, especially in psychology. Many are attracted to the emphasis placed on this life and on our actions, rather than on faith and the threat of a negative afterlife. Speaking of the afterlife, most converts I have spoken with were comforted by the idea that Jews aren't the only ones who go to "heaven." Some people are refreshed by the lack of an intermediary between the individual and G-d and that rabbis are simply "teachers." Most converts seem to enjoy the freedom to ask questions that is not only encouraged by Judaism, but required.
Family issues: Jewish fathers, mothers converted in a movement before your birth that happens to be more "liberal" than your current practice, other Jewish family members, Jewish significant others past and present, wanting to create a unified religious upbringing for your children, and surprising genealogical discoveries on Ancestry.com.
Community: You may love the community you live in now, but you need to be able to survive without this particular community. You'll likely live in a different community before you die, and especially if you're an orthodox conversion candidate, you may have to move to a different community simply to finish your conversion!
Ritual: Maybe you feel a deep and unnameable connection to one or several rituals/holidays. The language of symbolism often speaks very effectively to our subconscious. Many converts find comfort in the ritual, predictability, and structure of Judaism.
Jewish Coincidences: There isn't a much better word for this idea, but I've frequently heard/read from converts that as they look back on life, they can't see how they could have ended up anywhere but Jewish. Even myself, I see the pieces of the puzzle coming together over the years, but I had no idea at the time!
Ultimately, when all these reasons mix, the answer to the question, "Why are you converting/did convert to Judaism" comes down to "I couldn't be anything else." But maybe now you have the words to explain how you got to that point.
Some negative motivators might also be present. They are probably not deal-breakers because they're rarely the only reason you're considering conversion, but you should recognize them and deal with them.
- Unresolved issues/anger with your family of origin or religion of origin
- Pressure from a significant other and/or his or her family
- Being eager to please a significant other and/or his or her family
- The desire to "fit in" with friends or family
- Pressure from the greater (or local) Jewish community if you're in an interfaith relationship
- Pressure from psychologists or other members of the wider public to give your children a unified religious upbringing
- Idealistic stereotypes of Jewish families and how they're better than your family of origin
- Dissatisfaction with yourself. As written in The Intermarriage Handbook: A Guide for Jews and Christians, "Conversion should feel like a chance to become more fully your real self, not like a chance to transform or to leave your old self behind."