We’ve got a lot of messages about this in the past few days, most of which asking whether Jake’s distance from his kids makes him bad. The writers are definitely taking a close look at a bunch of fatherly relationships this season. Each one is different and deserves its own analysis to try and see what the writers are trying to say.
Jake didn’t have the opportunity to raise his kids for very long [as we pointed out before, he tried raising them for two days in Jake the Dad, but by the time those two days were up, they were already physically older than him].
At the end of Ocarina, we see Kim Kil Whan, already living with a woman and with a picture of his own child sitting beside him, talking about Jake exactly the way a parent would speak about their own child.
Their particular father-son relationship is almost inverse, and they’re struggling to accept that Jake is Kim Kil Whan’s father, when their relative maturity might make it appear otherwise. Kim Kil Whan appears to accept this at the end of the episode. Although Jake is goofy and not much of the ‘parent type’, he still cares a lot and means well.
The tension in Jake’s relationships with the rest of his kids hasn’t been quite so neatly resolved yet, though. The last we saw of TV and Jake Jr. showed them pretty angry with him for being late with the food to their party, and Kim Kil Whan beamed Jake away before they had the chance to talk.
We don’t know the circumstances by which Martin left Finn as a child, but all indications from his appearance in Escape From the Citadel show that he sees his own well-being as being more important than helping Finn. He manipulates Finn to heal his vaporized leg, offering what he knows full well is probably what Finn wants from him.
He then abandons Finn and Jake to deal with the Lich on their own as he tries to escape. Finn, of course, tries to keep him from leaving, and the writers don’t leave much ambiguity about Martin’s role as a father. His self-interest leads to negative consequences for his son.
We know from Giuseppe’s poem that he has strong regrets about something that happened between himself and his daughter. The poem is accompanied by a pretty morbid image of daughters apparently mourning their fathers.
"These are not my teardrops, daughter dear, but just the sheen of dew that lingers here. Past other fields where other fathers lie, who kept their daughters better far than I." We think this might mean that his daughter actually died, and he is left to mourn her instead.
We don’t know much about his circumstances beyond this poem, but Giuseppe appears to be a father that means well, as Jake does, who also couldn’t be the father that he had perhaps hoped to be.
Just judging by these few examples, the writers look to be saying that it’s tough to be a good parent, and there’s a lot of things that threaten to get in the way of that.
It’s tough to come to an absolute conclusion on what exactly the writers are trying to say here, though, when we still have only an incomplete look at the season. There’ll definitely be more episodes touching upon the fatherhood theme this season, with an episode following Finn and Jake’s parents before Jake was born on the way and [spoiler alert?] both Ice King and Marceline voice actors teasing the plot of an upcoming Ice King episode.