That right there? That's a man of principle. A guy that learned at a young age that all home run balls hit by the opposition are to be thrown back on the field, and - more importantly - a guy that won't let his girlfriend's incessant need for a souvenir compromise those teachings. If she wants a new toy to put in her purse until she gets home and completely forgets about it then he'll stop at the team store and buy her a novelty baseball for 4X the retail price, but he would rather leave single than leave with a Cleveland keepsake.
That's a dedication to his fandom that I can't help but respect, because there's a pretty good chance that this chick flipped his refusal to give her the ball into some stupid argument about how he cares more about the Mariners than he does about her. Probably used the walk back to the car to cultivate this toss-back into a metaphor for their relationship. In the warped brain of a woman that ball somehow represents 'trust' or some such shit. It may not get brought up today or tomorrow, but the next time he leaves the toilet seat up after she watches an episode of 'Girls' he will be hearing about this again. In that moment he might even regret throwing it back but in this moment he knew it was the right thing to do and he didn't let a whiney and - dare I say - abusive girlfriend stop him. I can tip my cap to that level of team loyalty.