The problem is that the politics are not partisan and instead divide the main parties.
It would be similar to half the republicans and half the democrats agreeing on a key policy & fundamentally disagreeing with the other half of their respective parties.
(it's actually even worse than that because there are at least 3 main positions [hard exit, soft exit, no exit] which divide the two main parties, meaning nothing really has a clear majority).
The way the UK government works is: from the majority party a government of ministers is formed from their group of MPs. By convention individual MPs in this government (called front-benchers) have a cohesive support for the overall government policy (if they disagree with the policy or vote against it then by convention they have to resign). Anyone from the ruling party NOT on the front-bench can (and often will) vote against the government.
Brexit has been insanely divisive. Internally, the ruling Convservative party have at least 4 different positions, including the official government one. Many front-benchers have resigned.
Fundamentally the problem is this; people voted for Brexit. But only just. So really nearly half the population doesn't want it. It was simple to answer a simple yes/no question. But exiting is a hugely complex question whereby it is nearly impossible to negotiate a compromise that works for everyone.