As a long-time veteran of the Led Zep/Page wars on the internet against people who have the audacity to publicly express that they don't find Page to be as good as his reputation, I applaud your entering into the fury.
It seems that there are many Led Zepplin fans who are like the worst St. Louis Cardinal fans I know- if you don't revere them, they jump to saying you are bashing, hating, attacking them, and that you are ignorant, stupid, or illiterate. My feeling is that Page falls into (to paraphrase the old Playboy Magazine jazz poll category) "Recognition deserving wider talent". He's a master or creating great riffs. He's a tremendously astute record producer. He can be an interesting guitarist, especially "rhythm guitar" or background beds. But he's not a great soloist. I can take slop if it has passion and emotion driving it (witness Neil Young on the SNL performance of "Keep On Rockin' In The Free World" with Charley Drayton on bass). But so much of what I've heard from Page fans trying to convince me of his genius is slop without redeeming passion coming through. My favorite Page solos are the carefully composed ones on "Whole Lotta Love" and "Stairway...".
The other thing is that I don't think Zep wrote good songs. They made great riffs, and wonderful recordings. But the songs don't hold up without those specific performances, and that's a bad song. A good SONG is NOT the performance, a specific solo, a specific vocal delivery, or a specific recording. A good song can be presented myriad different ways and still get across. "Stairway..." for example is a just about perfect record. The very cool and interesting contrary motion of the classic acoustic intro is great (especially if the D is played right the the F# in the bass - to keep the critical descending bass line of the part going). But the lyrics are worse than the most pretentious and silly Yes lyrics. Ending this huge anthemic build up with "to be a rock and not to roll" is as putrid as "I'll be the day your way"...
Zep's music evokes a time a culture, much like Hendrix does for a (slightly) older group- but Page as a guitar god just falls short of the people with whom he's most often grouped- Jeff Beck, Hendrix, and Clapton (fully understanding how and why many people can't fathom Clapton's reputation/esteem even though I think he's a critical component in the instrument's place in music.
Just don't label people how don't like Page, or have the temerity to publicly express what they see as short-comings as "haters". Most have opinions that are far more nuanced than that.
John