Welcome to worldbuilding, please give a good read at the help center: you are supposed to give your question a closed scope, not "anything goes" like it is now.

Hello Edgar. One of the most important rules on the site comes from the help center, where it says, "When asking questions keep in mind that the goal of the site is to help you build your world, not to tell your story." The help center also says that questions can't be hypothetical or open-ended. What this all means is we can help you determine a reason independent of any story you're trying to tell only if you provide goals, conditions, and limitations that help focus the question down to a finite list of answers. Those two help center pages are important to read.

Define "leave the Earth". If you are saying "why do they don't have satellites, why do they haven't explored the Moon", that's a thing. If you're saying "why haven't they colonized the Moon and terraformed Mars? Why do they haven't expanded through the galaxy?" the answer is for the same reasons we are not going to do it: it's economically ruinous even if there were enough physical means to achieve it - and they may never exist: FTL isn't possible and antimatter or fussion may be unatainable or improductive.

xkcd.com/893

Is FTL possible in your universe?

You're describing real life. Humanity already has advanced AI, superconductors, and laser weapons, but we are all still very much "on our planet", with a few temporary exceptions.

Are you wanting to extrapolate from our current state? Or from an alternate history prior to the Space Race? Or is this an alternate Earth entirely, perhaps with different physical properties? You should include more details in your question.

Where would they go? Flying off into the abyss with no destination in sight ... probably not the best idea. How would they get there? Space flight is hard, and there's radiation and stuff. We haven't even found any other planet where we'd know how to survive on yet, and any we do find would probably take quite long to get to. Why would they want to leave? Okay, there will probably always be enough people who want to explore, but you still need governments and/or companies to throw lots and lots and lots of money into the effort.

Where I live, humanity has advanced ai, superconductors, laser weapons etc. Just saying...

en.wikipedia.org/wiki/The_Road_Not_Taken_(short_story)

Do you mean they haven't gone to other planets, or they literally have no capacity to go outside the atmosphere or into space at all, in any way?

@Rekesoft, alas, we're working on colonizing Luna and/or Mars. (Terraforming, OTOH, is a whole other ball of wax.) Unless something happens, we likely will have colonies by the time we also have "advanced ai, superconductors, laser weapons etc." (and, no, we don't have those; not anyway in the sense I expect the OP means). Unless we're talking about alternate history, that ship has already cast off its mooring lines.

@Matthew: There's a difference between having a few research bases in a place, such as Antarctica, and actually colonizing it. It costs a lot of money and effort to maintain Antarctic bases, in a place where you have breathable air, can melt ice for water, and food & medical care are only a airplane flight away. They're nowhere near colonies.

Some less popular answers reflect my thoughts. Simple answers can be good. There is no real good reason to send humanity to space, It's expensive, dangerous and with advanced AI and unmanned probes one can get all necessary information for research. If their planet is in a decent shape and the population didn't explode why go further.

Most obviously, because there was never a real reason to try for space travel. Kennedy's speech amounted to little but propaganda. In his case, true in every detail… and so what? Your people should remain on their planet until they have a genuine reason to try for anything else

If you do not have FTL, there is not much point to space travel to other solar systems, and even inside our solar system, the physics dictate that there cannot be space 'travel' as such, but rather space 'awkward, costly, time-constrained, lenghty, dangerous, hopping'. Basically it's economics. If you cannot find a valid reason for the huge expenditure of lifting stuff into orbit and beyond, you don't do it. Without national pride, no one would have thought to send people into space. so maybe add a reason (Why did they not, in the face of XY need...)

Despite that general answer is historical reasons, and that most of the answers are bad inventing a plot for op, but I would prefer to keep this q open as indeed it would be better provide better reasons or point out problems of such activity, I mean difficulties it has - better answers would help to create better fiction instead settling on low-quality reasons, which accepted answer is an example of.

They could be too interested in themselves to worry about the stars or anything truely bigger than themselves. Or it's like a dictatorship where they don't want any art because that involves out of control thinking

Isn't that backwards? Wouldn't it be more realistic to completely ignore the very idea, on the grounds that there's no reason your - or any other - species should have space travel?

A very good, very simple answer - make Earth heavier. Not by much.

People will always want to fly.. and travel to space. It's part of our dreams, you can't just suppose there is no reason to fly, or no incentive to go to space. There must be a blockade of some kind. They can't, won't.. don't dare to.. are too fragile..