Liberal is well defined in virtually all models of classification used in political science and political philosophy, which a project such as this should probably defer to.
Also, the reductive "then we should toss out the word 'logic' then!" kinda comes off as a tantrum, to me. I don't really get the point. Why not focus and possibly disagree with the suggestion that nobody agrees on what "a liberal" means?
If you try to switch the argument to your analogy, then you're going to spend more time defending and explaining your (nonsensical) analogy than you would just explaining where you disagree. For example, you'd have to start explaining why you think people disagree about the word "logic", something I've never encountered.
Not a very effective strategy.
>I don't really get the point.
The point is that it doesn't matter if people in general don't know that the word means, which is why I didn't refer to "people" but classification systems designed by and for people trying to understand political ideologies and orientations. The term "liberal" has definite specific meanings that correspond relatively narrowly.
> something I've never encountered.
Then you've never asked regular people what logic is or haven't noticed that their answers differ widely and hardly correspond to what philosophers and mathematicians mean. Nevertheless, the laity's ignorance does not dilute the meaning of the term.