Snape's actions were ultimately heroic, despite personal animosity.
Yes, he treated Harry harshly and unfairly in class. He didn't like Harry, but risked and sacrificed everything to help him anyway. It's actually more heroic to help someone you don't like, because you know it's the right thing to do, than to help someone you love.
It's also a little overly simplistic to say that Snape saved Harry "only because he had Lily's eyes and if he didn't Snape wouldn't have". Yes, Snape's initial motivation to switch sides was entirely personal and revolving around the woman he still loved. But he continued to fight for the good side, even when they all hated him and thought him an enemy, long after her death. He did what was right, even when (after Dumbledore's death) literally no-one thanked or appreciated him for it.
It's perhaps also not entirely accurate to say that Harry liked Snape. Their relation was never friendly, and Snape was always unpleasant when dealing with Harry directly (although it would have been very interesting to see how this would have developed if Snape had survived!) But Harry certainly respected and honoured Snape after his death, even naming one of his sons partly after him. It takes maturity to recognise that someone you always disliked personally was nevertheless a hero.
Whether Snape was ultimately a "good" or "bad" character is one of the most controversial questions in all of HP fandom. But it's a little one-sided to see him as just a bullying teacher who helped Harry only because of his eyes.