A father figure is not a literal father stand-in.
A father figure can be a teacher - heck, a brother.
Anderson has helped and guided Shepard at the times Shepard needed it most. It is actually (IMO, though I know I may be looking too deep into things) very appropriately symbolic when on Vancouver Anderson stops Shepard from plummeting into the pit.
He's a reminder that while everything hinges on Shepard - no matter our RP, Shepard does depend on some people in some ways to survive and get his job done. And Anderson partially is relied on as a mentor. You can expand how much of a mentor Anderson is, but he's always somewhat one.
Of course Shepard surpasses Anderson quickly enough in even ME1, but ME3 is supposed to be the time of Shepard's doubts and weakness (in some ways), so Anderson is propped up again as the resistance fighter and Shepard is supposed to make him proud. You can minimize the presence of this kind of thing, but its a part of the core narrative that we can't completely avoid, like with our sorts of interactions with TIM, Liara, etc.
ME3 is a 'best (or rather, okay) place to start in that it actually rehashes some elements of ME1. The relationship with Anderson is kinda that, and taken to another level.
No, Shepard doesn't really see Anderson as his father, figuratively or literally. But he does always, to an extent, whether the player likes it or not, look up to Anderson and his accomplishments, morality, duty, and initiative, in the son-father relationship archetype. This is only barely there (but there nonetheless) in ME1 and ME2 and Bioware decided to focus on it and grow it as a more prominent fixture of the narrative in ME3.
While it can be argued in the canon that TIM set up Shepard's journey and propelled it forward, it was Anderson that made that journey happen more personally, and whose character and actions ensured it could even be propelled. We're (generally) to give more of an emotional damn about Anderson, he is 'family' compared at least to TIM, regardless of more logical conclusions about TIM's cause-and-effect resulting in Shepard being alive and using the tools he uses to win.
EDIT: A reminder that ME3 is on the backdrop of an extinction level war. I think the dramatic point being made in all sorts of events and relationships in the game is that this is basically the suicide mission for the galaxy. It encourages many to find family in each other, even if not literally and not permanently. Reapers arriving --> Shepard looking for more guidance from Anderson. Even the 'unbreakable' and 'personality-less' (at least when looking at ME1) Shepard doubting his abilities and judgement and using Anderson as an example to push forward. Not all the time. Not in a hugely overt way. But yes, when Shepard and Anderson are dying next to each other, they sure as hell are going to look to each other for emotional support in a semi father-son way.