The primary objection that freewill theists raise to Calvinism is a moral objection. They say Calvinism is morally repugnant. Moreover, freewill theists like Jerry Walls routinely accuse Calvinists of deceptive rhetoric to conceal just how awful Calvinism truly is.
Here's a recent statement by freewill theist philosopher Victor Reppert on the problem of evil:
Well, I personally would rather live in a world in which children are raped than in a world without free will.
But I suspect you will find my preference repugnant.
A world with childrapists raping children is a better world than a world in which they are prevented by God from raping. Yes.
For some readers, especially rank-and-file freewill theists, it might be shocking to be exposed for the first time to stark implications of their own position. Have you ever heard Jerry Walls or Roger Olson say something like that?
Although most freewill theists aren't as blunt or forthcoming as Reppert, his underlying position isn't idiosyncratic. It's just the particular example that's so grating.
A freewill theist is committed to the proposition that many horrendous moral evils in this world are divinely preventable. Assuming divine benevolence, they have to say that God doesn't intervene more often to prevent them because a world in which God did so would be worse overall. It would sacrifice some greater good.