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ELI5: Why is √4 = -2 false?

Maybe this is kind of dumb but I'm in algebra 2 and we've been doing a lot with square roots and radicals. And for most of what we've done, we'd get something like

x^2 = 4

x=2, x= -2

But when checking for an extraneous solution, it worked out to -2 = √4. I figured that worked, so I entered -2 as a valid solution for x, but the computer marked me wrong. I asked my teacher, and she told me that basically

If you have x^2 = y, then the answer is x= ±√y

But if you have √y = x, it's just the positive number.

But aren't x^2 = y and x = √y pretty much the same? Why does it work one way but not the other?

Why is

-2^2 = 4 valid, but -2 = √4 false?
gpt
It’s really just convention that sqrt(x) only means the positive square root. You’re right that 4 has a positive and negative square root, but we write +-sqrt(4) to mean 2 and -2, whereas sqrt(4) just means 2.

However, when solving the equation x^2 =4, we include both solutions 2 and -2 unless there’s some other information that tells us that x can’t be negative.