The Doctor has gone home to Gallifrey occasionally, though usually reluctantly. At different times, he's expressed different reasons for not wanting to go there.
The most consistent reason, over the years, has been that he just doesn't like the place -- or, rather, he doesn't like the Time Lords who live there &, especially, he doesn't like their politics. They also, repeatedly, manipulated him for their own purposes, which made him dislike them even more.
Initially (First & Second Doctors), he couldn't control the TARDIS well enough to get to Gallifrey & he was also both a criminal -- having stolen the TARDIS & having interfered in other peoples' histories -- & a renegade who rejected normal Time Lord society.
For much of his third incarnation, he was an exile on Earth, without a functioning TARDIS, so again wasn't able to go to Gallifrey. After his exile was lifted ("The Three Doctors"), he still had his dislike of Time Lord society & had added to it his lingering resentment over having been exiled & deprived of the ability to explore time & space in the TARDIS.
During his fourth incarnation, he was summoned to Gallifrey (at the end of "The Hand of Fear") & found himself in the midst of Time Lord politics (in "The Deadly Assassin"), which reinforced his dislike of Time Lord society. A later visit (in "The Invasion of Time") again involved him in Time Lord politics.
In his fifth incarnation, he was abducted to Gallifrey (in "The Five Doctors"), along with previous incarnations & several past & (then) present companions -- Time Lord politics again.
In his sixth incarnation, he was put on trial by the Time Lords in what he considered (rightly, as it turned out) to be extremely unjust circumstances -- Time Lord politics yet again.
During the Last Great Time War, when he was in his eighth incarnation, he tried to avoid participating in the war, because he regarded the conduct of the Time Lords to be almost as bad as that of the Daleks, whom they were fighting. In the course of the war, having learned how hated the Time Lords had become, he crashed on Karn (in "The Night of the Doctor") & regenerated into his ninth incarnation (the War Doctor), who stopped using the name Doctor & fought to end the extreme horrors of the war -- horrors for which he blamed the Time Lords (especially Rassilon) at least as much as he blamed the Daleks.
In his tenth (Ninth Doctor) & eleventh (Tenth Doctor) incarnations & the earlier portion of his twelfth & -- because he'd used a regeneration without changing from the Tenth Doctor -- final incarnation (Eleventh Doctor), he believed Gallifrey had been destroyed (by him) & that, because the Last Great Time War was time locked, it was forever inaccessible.
When, as the Eleventh Doctor, he learned (in "The Day of the Doctor") that Gallifrey had not been destroyed, he also learned that it had been saved by being "hidden away" in a "parallel pocket universe" & was, therefore, still inaccessible. Towards the end of that incarnation (in "The Time of the Doctor"), he learned that the Time Lords were trying to bring Gallifrey back into the main universe, running the risk of reigniting the Last Great Time War, with all its horrors. The Time Lords granted him a new cycle of regenerations but he didn't help them to bring Gallifrey back.
In the first (Twelfth Doctor) incarnation of his new cycle of regenerations, he discovered both that Gallifrey had returned & that the Time Lords had -- yet again -- manipulated him (& others) for their own purposes.
He was left with his original dislike of the Time Lords & their ways, now strongly reinforced by extensive, bitter experience of those ways. Therefore, he doesn't go home unless he really has to.