I believe the point is multifaceted:

1. Relationships are hard.

2. If you take a step back and look at the things you argue with your significant other about (or anyone else close to you), it's humbling to see how silly it often is.

3. Love doesn't always agree; if you actually hated the person, why would you stick with them through the annoyances and arguments instead of leaving?

Sure, the whole thing seems unhealthy and petty, but I think that he would have stopped writing a lot sooner if he didn't truly love her. I also think the slightly-hidden image at the very bottom left of the page says a lot more than any of his words do.