It's also because a large portion of Liverpool fans are Irish or have Irish heritage.
I'll also pick up on your comment on Gerrard, singing the national anthem =/= being a proud englishman. Different players do different things to "get in the zone". Doesn't make the Englishmen any more or less patriotic than the great English heroes Terry, Cole, Barton etc.
I just think it does't hurt to sing the anthem, like I said if your fans have that view then it wouldn't surprise me if Gerrard shares that.