Learn English – Walls closing in

I like to think introduces a pleasant or hopeful wish, but with some uncertainty.

I like to think that people are mostly good.
I like to think that I'm good in bed, but how should I know?

Rhetorician has pointed out correctly that this phrase is a quotation from the Bible (Romans 4:18), or, more precisely from the 17th-century King James version (“Who against hope believed in hope..”). The Greek original has: ὃς παρ᾽ἐλπίδα ἐπ᾽ἐλπίδι ἐπίστευσεν, where the Apostle plays with the double meaning of ἐλπίς, which can mean both (positive) “hope” and (neutral) “expectation”. In older English “hope” also had both meanings, but the latter is now obsolete. A modern English literal rendering might then be: “Who against expectation believed in what he hoped for”.