OK, for the sake of argument, I'll play along with that game.
Suppose that ending the life of someone who is suffering is indeed loving. True love, of course, will do anything for the beloved, no matter the cost. Assuming that you do think that euthanasia is indeed loving, are you willing to forsake everything to accomplish that act? Are you willing to sacrifice your career, fortune, property, inheritance, freedom, and even your very life itself for it?
No? Well, then that isn't love.