You cannot measure 120 AC with normal scope+normal scope probe !!!!
Can you explain?
But yes, if you talk for noobs, yes stay away from live mains with normal scope with normal probes (even when they can use if really know things and understand these things)
Educated professional can use normal CAT II 600V rated passive probes for 120 - 230VAC (if environment/circuit is CAT II class and follow all safety instructions and rules)
Today I'm retired but after ~1970 I have done it thousands of times including real industrial professional work except that here we have 230Vac mains. We do not stay there for playing, our job is keep factory running 24/7/365 even when some things need repair "on the fly". I have get also HV working safety education and education for maintenance and repair work on live installations. Even when my main job have been with electronics and automation.
But, I do not recommend anything with danger voltages and danger currents for uneducated hobbyists or even professionals who do not have special training for working with live high voltage circuits. And of course we use there also more safe HV probes when need, or other methods, depending situation. But claim that these normal probes can not use for 120VAC (if also look that other related things are still safe) , it is false - if only definition is this voltage.
Yes I can explain. I take the normal probe, and (with a tongue at the right angle) i look at the power outlet. I have this one pointy thing and a crocodile thing... And then I randomly (Russian roulette style) decide which one I stick to the left hole in the outlet and which one to the right.
Because, power outlets are NOT defined which one is live and whic one is neutral. Even if you stick grounded side of the probe (scope) to the neutral, there is no guarantee there are no stray voltages between power neutral and earth circuit.
So basically pure luck if it goes boom.
I have normal (grounded) 100x probes that I use on 1000V on a grounded circuit inside device.
And I also had occasionally measured something on a primary side of the switcher. With probe safely connected to grounded side of circuit.
Once, a crocodile slipped, and on it's way to the desk it touched live circuit. It was old school Hitachi scope, it survived, mains fuse was blown, and I was the village idiot for some time until somebody else made something stupid and my colleagues moved on, making fun of somebody else..
Point is, even if you exactly know what are you doing, there can still be mistakes.
And OP, by it's own admission (it is a sign of a smart person to know your limitations) is a complete beginner.
So, yeah, I stand by what I said. In these circumstances I gave him best advice.
I make it a point to make a distinction between what is possible and what is a smart way to do it.
If you take a stick of dynamite and a lighter, and slowly heat one point of the stick, dynamite won't explode. It will, in fact, start burning with a yellowish smokey flame and quite slow. You might use it as a torch... Despite that fact, smart people will probably want to use a candle or a battery hand torch for light.. It's kinda less extreme.