Why He's the Greatest: Though he "only" has 11 Grand Slam titles to his name, it'd be pretty hard to match the achievements of any other player on this list with Rod Laver's and come out with a favorable comparison.
Laver won his first major as an amateur at the Australian championships in 1960, his first Wimbledon in '61, and then captured the complete Grand Slam in '62. As these were amateur events and Laver, like all of us, needed money for food, he would not play in them again until 1969.
When professionals were again allowed to play in the Grand Slams, Laver duplicated his feat, winning the complete Grand Slam for the second time, something never done before nor since.
While he was winnning his majors, he also played doubles, unheard of in today's game. All told, he won 54 singles titles as an amateur, 69 as a professional before the Open Era, and 75 after the OE began: 198 total.
In 2006, Bud Collins, the unparalleled historian of the game, called Laver "in my eyes, the greatest player ever."
Why He Isn't: There will always be the argument, usually brought up by today's fans, that the game of tennis has evolved far beyond what it was in the late '60s, and that a man of Laver's stature (5'8") simply could not dominate now as he did then.
It's not just today's players who doubt Laver's GOAT status, though; many prior to the Open Era also were unconvinced. Despite Collins' above statement, he left room for the possibility that "Big" Bill Tilden was the greatest of them all, and said that Pancho Gonzalez would be the one player he'd want to "play for my life."
Some other greats didn't even consider Laver the greatest Australian: The American Don Budge admired Laver but gave the nod to Jack Kramer. Gonzalez considered Lew Hoad the best.
Kramer, interestingly enough, thought the best was either Budge or Ellsworth Vines.
As these players come from eras when the Grand Slam events did not provide the barometer as they do today, their claims are difficult to either prove or dismiss.