People are upset partly because the new administration is taking the law into its own hands, and partly because it seems to be acting without any planning or research, and seems to be going about it recklessly and without concern for consequences.
Regarding USAID specifically, it was set up in the aftermath of the Foreign Assistance Act by John F. Kennedy, and as an agency it was later established as law by Congress. Trump cannot legally shut down USAID without another act of Congress, and he cannot legally redirect its funds, which have already been appropriated. The administration is well within their right to change how the funds are allocated, but so far the stated intention has been to shut off all foreign aid, not change what aid is provided.
The fact that Warren Christopher etc. wanted to get rid of USAID 27 years ago is irrelevant, since that plan was never adopted and did not call for shutting off foreign aid, so it's not comparable. It's just misdirection.
It's also difficult to take arguments for "government waste" seriously in the case of USAID. First, the agency has a tiny budget of around $50B (2023), 16x less than Medicare, or around 0.8% of the entire state budget. Secondly, it was explicitly set up to give away money. Waste is its raison d'etre! Reports show its admin overhead being around 7.7%, which is very low for an aid organization.
It's pretty clear that USAID isn't cut because of waste, but because the Trump administration wants to stop giving aid to poor foreign countries. However, they're not so inclined to say that out loud.
It's also a self-own because USAID is an important soft power tool. It's one of the ways the US can project a positive image on the world, something it has been very good at since the post-war period.