As you may guess by my current avatar, I support the idea that someone has control over their own body
I own my body and, therefore, should have the right to terminate it. However, you are right regarding mental illnesses, which is why I don't think it unreasonable to require that a person go through a degree of psychological testing before being approved the courtesy of ending their own life, much like is done with sex changes.
Incidentally, I think this has nothing to do with our culture's respect for life, but has everything to do with our cultures respect for self-liberty. In the case of abortion, from the perspective that it is a life (and I know this is debatable, but I'm not arguing that point), that life has ownership of its body and, therefore, another person does not have the right to take it. Likewise, I have ownership of MY body and DO have the right to terminate it. So, if you hold the belief that life is precious and, because of this, are against abortion, supporting euthenasia has nothing to do with that IMO.