After Liverpool performed so well in the group stage of the UEFA Champions League competition, a lot of people believed Liverpool was the favorite to win the UEFA Champions League trophy because no club's performance matched that of Liverpool's performance, so it's normal for your friend to boast that Liverpool will win the UEFA Champions League trophy.
You're right anyone can harbour such mindset that Liverpool was going to win that UEFA league for last season considering there performance from the group as you said not even only that, as that time, the same Liverpool was excellently doing well in their domestic league too which was also a yastuc anyone could use to validate his or her assumptions to this effect but unfortunately they weren't able to achieve that, I think PSG prioritized the UEFA champions league games last season because for me I never thought the will qualify they were to face Liverpool although they got lucky but that was because Liverpool weren't seen as a serious team in the second leg of that match although that's now history.