IDF is the military branch of an actual state. Likud is a political party. Neither advocate for indiscriminate killing of civilians (though some Likud politicians might, just like the US or any other nation has crazy politicians).
"Right to exist" is granted either through law or force. Hamas doesn't have law, doesn't exist within a functioning state, and is illegal by the laws of most nations. IDF isn't.
If you actually think there's a moral equivalence between the IDF and Hamas, or that Hamas is somehow the moral group here, you really need to learn more. Stop consuming social media, stop reading things on the internet, go buy some books from a diverse array of sources, both pro-Israel and anti-Israel, and maybe you can gleam the truth out of there. It's not a guarantee, but it's your best shot.
I really think the TikTok age has amplified insanity where we actually have people asking, "Why does a military get to exist but not terrorists?".
For anyone who needs a reminder of how this war started (warning, extremely graphic / not suitable for life): https://www.hamas-massacre.net/