The better arguments tend to focus, as this one does, on the fact that a lockdown does not come without its own harmful ramifications: delaying health interventions, increases in spousal/child abuse, increase in depression/suicide, loss of income/insurance, loss of financial stability, etc. I'm not necessarily saying that these arguments are or are not persuasive, but they're looking at the right things.
The worse arguments tend to focus on the lockdowns depriving Americans of their God-given freedom to attend pool parties and political conventions, regardless of the epidemiological data.
Unfortunately, many of the people who are really motivated by the latter tend to use the former as cover. (This doesn't just pertain to COVID-19, but to a lot of controversial issues.)
Generally, when you can reasonable predict that your argument may invite some unwanted bedfellows, it's nice to toss out a disclaimer -- something like, "Now I know some people will seize on my argument to advance X, which I reject, so let's talk about the limits and bounds of what I'm arguing." That way you can make it clear that you're not willing to let your remarks be used in ways that you don't intend.