Hagrid is one of the most consistent and reliable father figures Harry Potter encounters over his lifetime (though that's not saying much when many of his other father figures are examined in detail). Still, Hagrid supports Harry because he genuinely cares about him and he should get credit for that at least.
But Harry doesn't end up naming any of his children after Hagrid, and that may be because Hagrid gets to be less reliable as Harry grows up. Hagrid is big and magical when Harry meets him as an eleven-year-old, but that's not quite enough as Harry grows and nears the end of his journey.
Not Being Clear
Hagrid is not always the best communicator, and his lack of clarity often harms Harry more than it helps. While Hagrid not specifying exactly where Platrofm 9 and 3/4 is after giving Harry his train ticket ends up not being too terrible for Harry, Hagrid's clarity issues become more of a problem as Harry grows up.
While Hagrid gets Harry and Ron to "follow the spiders" he also almost gets them eaten by those same spiders. That's a much more dangerous lack of information than the platform location ever was.
Drinking
Hagrid's drinking is what helps to win him Norbert the dragon in Harry Potter and the Sorcerer's Stone, but it's also what gives Voldemort access to the Sorcerer's Stone.
While this doesn't harm Harry very much in his first year, Hagrid's drinking becomes more of a problem as Harry has to address it. Hagrid drinks after Buckbeak escapes. He also drinks after the "secret" of his parentage is revealed in an article. Harry, still a student, ends up having to take care of his father figure rather than the other way around.
Lawless
Hagrid is always breaking the law. The fact that he still has the pieces of his wand in his pink umbrella and uses them to do magic proves he is breaking the law at all times.
While cursing Dudley with a pig's tail doesn't harm Harry, the fact that he thinks it's safe to have an illegal dragon in the house does. Harry gets detention, but he could have gotten injured. Hagrid's lack of respect for the laws that are meant to keep witches and wizards safe becomes more reckless as time goes on.
Fearless
Hagrid is big and strong, which makes him particularly fearless in the Wizarding World. He doesn't scare easily, and finds giant three-headed dogs adorable. This is very cool, especially for an eleven-year-old to see, but Hagrid's fearlessness often puts children in danger.
Whether it's having Harry help care for a dragon, introducing thirteen-year-olds to Hippogriffs, or blast ended screwts, he doesn't seem to understand how his size makes him significantly different from those around him.
Grawp
Hagrid's fearlessness and lawlessness come together when he brings Grawp, his giant half brother, home with him to the Hogwarts campus.
He hides him in the Forbidden Forest and thinks it's not only necessary but appropriate to ask teenagers to enter that forbidden space and help take care of a giant. It doesn't seem like, by book five, Hagrid has Harry, Ron, and Hermione's best interests at heart. He seems a bit adrift, and very irresponsible.
Can't Keep A Secret
Hagrid not being able to keep a secret helps Harry, Ron, and Hermione go after the Sorcerer's Stone. However, Hagrid's inability to keep secrets becomes far more problematic as the Harry Potter books and films go on. His inability to keep his secret about his parentage leads him into a depression.
His inability to keep a secret about the first task in the Triwizard Tournament leads him to not only help Harry but assist his competition (Fleur) as well. It stops being funny after a while and starts putting children in real danger.
Teaching Skills
Hagrid is genuinely surprised when no one wants to take advanced Care of Magical Creatures classes with him. While the Hippogriffs were exciting, and a good lesson (aside from Malfoy not listening to instructions) Hagrid isn't known for his teaching skills.
From the boring Flobberworms to the dangerous Blast Ended Screwts, students are either bored to tears or forced to tend injuries. It's hard to watch Hagrid fail so spectacularly even as Dumbledore promotes him.
Not Keeping In Touch
In the first few books Hagrid is great at keeping tabs on Harry. He sends him Christmas and birthday presents and is part of the mail that Dobby steals from Harry in Chamber of Secrets.
However, as time goes on, Hagrid sort of falls off the correspondence train, and Harry is left very much alone in the world (particularly during the summer holidays). As Harry needs more care he seems to get less and less.
Disappears
As with his correspondence Hagrid also starts to disappear on Harry. He is missing for a good portion of The Order of the Phoenix and, despite Dumbledore's insistence on secrecy, it doesn't make much sense that Hagrid wouldn't at least tell Harry he is going to be out of town.
Harry is desperate for connection which Hagrid offers and then, regularly, takes away. It's kind of him to tell Harry the full story of speaking with the giants upon his return, but it's not enough.
Trusting Dumbledore
Dumbledore stood up for Hagrid and kept him out of Azkaban (the first time) so Hagrid's loyalty to Dumbledore is understandable, but it begins to hurt Harry.
No one, Hagrid included, stands up for Harry when he is entered in the Triwizard Tournament, nor assists him as Umbridge is torturing him. Hagrid's trust in Dumbledore to choose correctly and address issues as they arise makes him less conscious of the damage being done to Harry as time does on. It's sad to see Hagrid's interest in Harry disappear rather than grow.