Republicans need to repeal the ACA at all costs because the ACA benefits people who do not support their party. That's the simple answer.
The ACA provides health insurance to poor people, who generally don't vote for Republicans. And people under 26, who generally don't vote for Republicans. And the unemployed, who generally don't vote for Republicans. Basically all of the groups that don't vote for the party of capitalist affluence.
Reason number two is that the ACA includes a 3.8% surtax on investment income above $200k/year. It's literally a tax on rich people, who ARE the party's core constituents. They're just looking out for their own.
So you see the problem. The ACA is perceived to be, on average, bad for Republicans and good for Democrats. That can't be allowed to stand.
That's it. There is no great mystery here.
All of the philosophical objections they have raised, such as "the individual mandate infringes my freedom" were previously addressed by the neocon Heritage Foundation when they proposed it in the first place, as a free-market solution to controlling healthcare costs. They rightfully pointed out that everyone uses healthcare, and anybody who avoids paying for it by refusing to buy insurance is a slimy freeloader and probably a closet liberal. It's that whole bootstrap mentality, self sufficiency and personal responsibility and all that. They said freeloaders shouldn't be welcome in America. They hate welfare queens and they hate people who don't pay for medical coverage, for the exact same reasons.
Now the law isn't perfect, by any stretch. The subsidies are implemented clunkily. Insurers aren't regulated enough. They delayed implementation of some important provisions for too long, and they allowed some states to opt out of a plan that really works best when everyone opts in. So I agree there is room for improvement, but it also got tens of millions of previously uninsured Americans into preventative care plans, it was 100% paid for with new taxes and spending cuts, and it reduced projected future deficits by controlling long term costs. It made health insurance incrementally better. It got a lot of things right, and I think we should be having a discussion about which parts we as a nation liked and which parts still need improvement, instead of a conversation about whether to repeal it on January 27th or March 14th of this year.