"He likes him."
Translation:Han tycker om honom.
tycka = to think, but only as in to have an opinion: "I think Duo is our god", "I think you're great"
tänka = to think in general , as in "I am thinking about Duo"
They're the one and the same in English, but two different verbs in Swedish: thinking something, having an opinion (tycker) and thinking of something (tänker)
All of this to say that the logic in "tycka om" is actually because of the meaning "to have an opinion":
"He has an opinion on her" ~ "He likes her" = "Han tykker om henne"