I would argue the love of argumentation is more of a Sophist ideal than a Socratic one. I think,  if anything, (as Plato demonstrated in  the dialogue THEAETETUS) Socrates was more interested in exposing what others didn't know (to get at what's true)  or more specifically bring forth what others take for granted and falsely believe they know. I think the discussion in THEAETETUS  146c – 151d
 of Socrates being a midwife is very telling in this sense:


"SOCRATES: My art of midwifery is in general like theirs; the only difference is that my patients are men, not women, and my concern is not with the body but with the soul that is in travail of birth. And the highest point of my art is the power to prove by every test whether the offspring of a young man's thought is a false phantom, or instinct with life and truth. I am so far like the midwife that I cannot myself give birth to wisdom, and the common reproach is true, that, though I question others, I can myself bring nothing to light because there is no wisdom in me."