jason never loved piper. i know i know this sounds kinda intense... and as i'm omitting the canon, but i'm right and i'm going to tell you why. since he can remember jason grace was instilled in the belief that if he was perfect people would love him, only if he was perfect would he be lovable. this philosophy is reflected in every aspect of his life, including his relationship with piper. piper mentions that she feels very guilty about not loving (at least that way) jason, because he does "love" her and because he is basically the perfect boyfriend (this has to do with my theory of lesbian piper btw). jason is perfect in every aspect of his life. this coming to make other people distrust him or think that he is boring, and well, here it's the same.
this boy is the perfect boyfriend because he thinks that with that he will be worthy of piper's love, which he never got, it could be that for the very fact of being so perfect or because simply piper is a lesbian. the thing is that jason never loved piper, he just wanted the love that he never got. he did not sacrifice with his life because he loved her, jason did that because he had to be the perfect demigod, the perfect boyfriend, the perfect boy. what kind of person would he be if he didn't sacrifice himself? well, here's the answer: someone not worthy of love, that's for sure. jason is who he is because his philosophy of life is "be perfect and you will be loved" he never felt love for it, he was never loved for it. jason grace does not know love for it, and this includes piper.