Why the push to follow EU nation's health care systems but be rabidly opposed to similar corporate tax policies?
Corporations have the resources to navigate tax loopholes that allow them to avoid paying their fair share of social responsibility, and any number of free market worshippers will regularly appear to say, "but of course, they have a responsibility to their shareholders to do so."
As a result of those two things together, corporate tax cuts are not popular on the left. If there were any evidence that high corporate tax rates were the root cause of financial strain for the average family in the US, or corporations weren't putting so much effort into dodging taxes, I suspect the left would care a lot less about whether they received tax cuts or not.
As it is, the situation has turned into monkeys and cucumbers (https://www.youtube.com/watch?v=meiU6TxysCg -- skip to 1:23 if you're in a hurry), and the left keeps seeing gifts laid at the feet of corporations in the name of trickle-down economics while social programs keep struggling for funding and more people keep needing social programs.
First, they're not opposed to a lower corporate rate per se. They are opposed to a corporate tax rate cut that isn't offset by some tax increase elsewhere.
Second, the de facto tax rate is well below the de jure tax rate, due to the giant mess of loopholes and tax incentives we've accumulated. There's support for bringing the rate down and closing enough loopholes to keep the actual tax burden more or less constant, but that doesn't appear to be what's happening.
Third, their view of the European model is of broad based individual taxes coupled with relatively aggressive income redistribution. Their view of the American model is of very top heavy progressively weighted taxes coupled with minimal redistribution. There's a lot of support to moving toward the European model, but only as a holistic transition. European taxes with an American welfare state is seen as the worst of both worlds.
Why? One of the ideas behind lowering taxes is to incentivize spending, which in corporate means expanding and, ideally, in the end, more taxes being paid overall, while the tax burden remains the same or lower.