Federer has intrinsic motivation, he doesn't need to be pushed by anyone. He plays any next slam like his life is on the line, it doesn't matter to him.
Federer had 16 majors and was nr.1 in 2010, Nadal only had 6 majors at the time.
Ok, if Agassi with 8 is not pushing Pete, then surely Rafa with 6 isn't pushing Fed.
You can put Fed in an era of nobodies and he would still win 30 majors, he gets extra motivation when he is nr.1, unlike most others who lose motivation and start cruising.
He loves being chased and being on top, he is so comfortable under pressure. I think Fed is pushing Rafa and Nole they have his slam record in reach. Plus Fed is not the kind of guy who needs titles for validation. I think that Nadal, Sampras and Djokovic all searched some life meaning in tennis, Fed didn't need that. Djokovic has finally realized records don't make you happy. Maybe Nadal should do that too.
Possible what you say. But there is a difference between Agassi and Nadal.
Agassi barely had 5 or 6 slams by 2000 and he was already nearing 30 when Sampras won the 13th. Agassi was also not a threat at the channel slams at all (FO and Wimby). There was no reason to believe old man Agassi would challenge 13.
Nadal was barely 24 in 2010. Yes, at AO 2010, Fed had a 16-6 edge but that same year, the edge got narrowed to 16-9 when Nadal was entering his prime and Fed was declining. There was every bit reason to believe Nadal would challenge 16.
Honestly, the rise of Djokovic helped Federer in a very ironic way. 2011 and 2012 were two of the very best years of Nadal's career and he was literally denied 3 slams by Djokovic (along with many other Masters tournaments). Still, Nadal had come close to 16-11 by FO 2012. Then, Fed won the Wimby and pushed it to 17-11.
Nadal had one more dominant year left, which also coincided to one of the Fed's worst years on tour. It was 17-13 at the end of 2013. No wonder that was around the time Fed found motivation to change his racket and also change strategies (more volleys, half volleys, sneak-attack-by-Roger tactics, the revamped servebot etc).
Don't get me wrong. I think Fed takes 20+ slams in any era, and in an era without Nadal, he takes 25 slams. However, I do not believe Fed would win slams at age 37 if Nadal didn't exist. I have a very hard time seeing just what could possibly motivate a man who would have won 25 slams to go with countless other records.