The world of Harry Potter is so rich and detailed that there's no shortage of little surprises all these years later. New angles and minor elements never noticed before can shed light on the Potterverse in ways we hadn't expected.
One of these interesting points was raised by amusingly-named Redditor ThereIsBearCum:
The reason Dementors are so interested in Harry is because he has 1.125 of a soul... Dementors go "shit yeah, 1.125 for the price of 1, gotta get me some of that."
Here's a relevant clip of a Dementor getting him (it?) some of that.
Let's examine this theory more closely. It seems from the books that Dementors are drawn more to human emotion than soul, although the two may be linked in some way that's never fully explicated in the books.
If Dementors want to slurp out happiness, they'd be better off heading for someone with a less painful past than Harry. Or maybe they feed on the fear caused by distorting that happiness, leaving people as broken shells. So many Dementor questions!
On a side note, the Potter math here is debatable. If we are to assume that splitting your soul across your Horcruxes distributes the soul evenly, then Harry would have received 0.125 — one eighth — of a soul. But who's to say that a soul fragments neatly like that when rent asunder by evil magic...
It's also hard to say that the Dementors are drawn to Harry in particular; he certainly gets attacked a lot, but this may just be the plot device of him being a main character. Or maybe there's some other reason that Harry's 1.125 soul is such an exquisite delicacy to Dementors. Suggestions in the comments please, folks!