there's a bunch of common answers to this question. as it is those answers are generally:

1. bogus when you actually think them through rationally. or
2. they're not well articulated but still not totally valid if one has a basic understanding of their risk tolerance and how the fund operates in the various market outcomes.

However even though the popular answers to the question are such, that doesn't mean that there isn't actually a good reason not to buy and hold LETFs. there are a few possibilities here, and it's not all mutually exclusive.

1. the people offering the non valid answers are primarily doing so out of stupidity. they just don't know the real reason why one ought not to.
2. or they're deliberately withholding the answer.

if i had to intuit a reason that was being deliberately withheld, what comes to mind is that they generate systemic risk in proportion to the percentage of total holdings they represent. and that such risk is not borne by the individual holders but by everyone in the market irrespective of whether they hold the LETFs. if this is so, then it would be an entire/y unconvincing argument to any individual not to hold LETFs. Tragedy of the commons.