So if your friend's distant relative killed your brother would you try to kill your friend? That's some of the logic that was just implied
But more specifically Madara was upset that Hashirama's father tried to kill Izuna when his father tried to do the exact same thing to Tobirama. Which seems like a crap reason to get angry if Hashirama can control himself.
So because Hashirama acted a certain way, Madara should act like that as well? They are different people (well, characters, but you get what I mean) so of course they are going to act different to a certain situation as well.
There's no rule that states that everybody has to react the same way to a certain situation - some people are more prone to react emotional than others.
Now it's already been stated that it's because of the Uchiha's capability for great love, that it's more likely for them to fall in the trap of hatred. If they lose someone they really love a lot (like Madara loved Izuna and his other brothers), they first develop the Sharingan and then later on gain the different stages if they go further. But with the development of their Sharingan, comes the big risk of them developing their hatred. Their love turns into hatred in some cases when they really go far with their development of the Sharingan.
I'm not saying that Madara is being fair when he said Hashirama had to either kill himself or his brother so they could be even. It isn't. But to him it seemed like a good solution. Family for family or the person himself.
Plus it was a war. Neither parties are eager to give in then.
Grief makes people do and say stupid things as well.
So while Madara wasn't right in demanding Hashirama either kills himself or his brother, it's a bit understandable if one takes into account the Uchiha's history with the Sharingan and the way they seemed to have a lot of clan loyalty.
But again, I'm not agreeing with what Madara said. It just isn't completely black and white.