We use relations in natural language constantly. An important thing about this predicate is that not is not symmetric, which means that xLy is not the same as yLx . In any case, with this sentence, what we're really saying is that for every individual, there's somebody that that individual loves. So, if you take anybody, you will always be able to find someone that that person loves. That's what we needed to say.
Somebody loves everybody.
This is different from the first one. We're no longer saying that every person has someone they love, we're instead saying that there's some person who loves everyone . That's exactly what we needed, and we're done. You can't love statements, as the attempted symbolization here tried to do.