First of all what must be established is whether the term "greatest" is a subjective or objective term. if it is subjective this surely isn't even a debate as you already have an opinion which i doubt i could change. However, objectively it is very clear Liverpool F.C. are not the greatest club historically or currently. Liverpool consistently fail to achieve national success especially against top Premier League teams. Their record in Europe is rather good for an English team, however they have less European titles than for example Real Madrid, Barcelona or Bayern Munich. Success could be measured in things such as the fans or charitability, However they fail on these characteristics too. their fans often have massive riot and the club donates less money to charity than clubs like Bayern Munich or Barcelona.
In conclusion I have been given no reason to assume Liverpool F.C. are either the greatest team in the world or anywhere close for that matter.