At first I was tempted to say it’s because we’re still in the League Cup and they’re not, and whilst that’s true, it’s actually a little more than that.
Even if you just look at the 3 league games over this period, we have games on the 19th, 26th and 28th. So gaps of 6 and 1 full day(s) without a match (I repeat, that’s ignoring the league cup).
Liverpool play on 19th, 27th and 30th, gaps of 7 and 2 full days without a match.
So they’d have an extra day on both sides of Christmas, even if we weren’t in the league cup still.