Dean being aro is just an headcanon, but I personally think that it fits well with canon. I am not mad at you for your message, don’t worry 🙂
Being aromantic means that you don’t feel romantic attraction. Attraction and behaviour are two different things: you can not feel romantic attraction and be in a romantic relationship, because not feeling that particular kind of attraction does not prevent you from enjoying kissing or dating or sex (btw, sexual orientation has nothing to do with being aromantic, which is a romantic orientation) or any other thing featuring a romantic relationship. According to me you just have to be honest with your partner about the fact that you don’t love them romantically, just in case they are not okay with that and/or there are some things that you don’t want from you relationship with them.
As for the way I view those two relationships… I can totally see aro!Dean in both cases, honestly.
With Cassie, from an aro Dean point of view it looked like Dean did care about her, but it was more of a sexual relationship than a romantic one. I didn’t see a difference between the way he acted with her and the way he acted with Charlie, nothing said that he was romantically involved except kisses (that don’t mean there was romantic attraction, anyway, just a romantic relationship). He did care about her, but he didn’t act like someone who was in love.
As for Lisa, again, I don’t see how Dean’s feelings about her are necessarly romantic. Dean wasn’t okay with that life, he wasn’t happy, always grieving Sam, especially at first. It was like he was just pretending, acting the way he was supposed to. He did try, but it looked a lot like a not-so-working relationship between a romantic and an aromantic person (as I have seen people describing them and as I have experienced them).
He never said “I love you” to neither Lisa nor Cassie and generally he doesn’t say it at all. My headcanon on this is that “I love you” is generally considered a romantic phrase, that can be used also platonically, of course, but generally media and society percieve it as romantic (English is ambigous here, in italian we have a platonic “I love you” and a romantic “I love you”). I think that Dean doesn’t love in that way, and he does realise that his love for Castiel is of the same kind he feels for Lisa, just minus sexual attraction. So he doesn’t say “I love you”, because it feels like he’s lying.
When someone is important for Dean, he immediately throws them under the “family” umbrella: Jo and Ellen? Family. Cas? Family. Lisa and Ben? Family.
Everyone is family, because no love is romantic for Dean.
Plus, Dean’s most loved person is Sam, his brother, a platonic bond. There are many researches that show that people who feel romantic attraction (also because of society) usually put their “significant other” above any other bond. With them, they build a new family that comes before friends and other platonic bonds.
For Dean, there’s Sam first. He dumps every romantic bond for being with his brother. When he looks at his future, he sees his family – his friends and brother -, not him settled with a girl. He tried that when he had only Lisa to turn to, and it didn’t work out, he wasn’t fit for that. Dean isn’t looking for a romantic relationship and had like two or three in his whole life, and he is perfectly okay with that. When Bobby tried to justify not telling him that Sam was alive because Dean finally had what he wanted (with Lisa and Ben), Dean said that he wanted his brother.
Dean has a big heart and loves deeply – I just think it’s not in a romantic way.
(Since I am afraid I haven’t expressed myself to well, here you can find some FAQ about aromanticism, here, here and here you can find discussions about aromantics in a romantic relationship)