All three agree, but by different amounts. I completely agree means you agree fully, with everything the person said — it's the strongest, and it's neutral, so it works anywhere. You've got a point is friendly and informal; it means you agree with one thing they said, not all of it. I see what you mean is soft and neutral; it means you understand their idea and partly agree, and it often comes before a small 'but'.
Agreeing
I completely agree — I completely agree. Trains are better.
You've got a point — You've got a point about the price.
I see what you mean — I see what you mean.
Not "I completely agree, but the price is too high." — say "You've got a point, but the price is too high.". Use I completely agree only when you agree with everything. If you agree with just one part and want to add a 'but', say You've got a point.
Try it: Amina: We should travel by train. It's better for the environment. Hiroshi: ___ It's much greener. Hiroshi agrees fully with Amina. Which fits? (I completely agree. / I'm afraid I disagree. / I'm not sure about that.) Answer: I completely agree. — I completely agree shows full agreement, which fits. I'm afraid I disagree and I'm not sure about that both show doubt or disagreement, so neither one agrees.
Disagreeing politely
These all disagree, but politely — from soft to softest. I'm afraid I disagree clearly means you do not agree; the words 'I'm afraid' just make it polite, so it's fine even in formal talk. I don't really agree is a softer, more informal way to say the same thing. I'm not sure about that is the gentlest: it means you have doubts about the idea, not a flat 'no'.
I'm afraid I disagree — I'm afraid I disagree about the time.
I don't really agree — I don't really agree with that.
I'm not sure about that — I'm not sure about that.
Not "No, you're wrong." — say "I'm afraid I disagree.". In English we soften disagreement. A flat 'you're wrong' sounds rude — I'm afraid I disagree says the same thing politely.
Try it: Sofia: The train is faster than the car. Diego: ___ I think the car is quicker. Diego politely disagrees. Which fits? (I'm not sure about that. / I completely agree. / You've got a point.) Answer: I'm not sure about that. — I'm not sure about that politely shows doubt, which fits Diego's disagreement. I completely agree and You've got a point both agree, so neither one shows disagreement.
Try it: Amina: The film was good, but it was far too long. Hiroshi: ___ It really needed to be shorter. Hiroshi agrees with only one part — that it was too long. Which fits? (You've got a point. / I completely agree. / I'm afraid I disagree.) Answer: You've got a point. — You've got a point agrees with just one part — here, that the film was too long — so it fits agreeing with only part of what Amina said. I completely agree would mean you agree with everything, including that it was good, and I'm afraid I disagree means you don't agree at all, so neither fits partial agreement.
Strong, gentle and too direct
These answers differ in how strong they sound. Strong agreement: Absolutely!, I couldn't agree more, That's so true! Gentle agreement: You're right, I suppose so (agreeing, but not keenly). Polite disagreement: I see it differently, I don't think so, I have to disagree. Save No way!, That's not true and You're wrong for friends — they sound too direct to a stranger or a boss.
Absolutely! — Absolutely! I love the warm weather too.
I couldn't agree more — I couldn't agree more! Everyone should learn a language.
You're right — You're right. Regular exercise helps a lot.
I suppose so — I suppose so, but I am not sure.
I see it differently — I see it differently — movies can be better.
No way! — No way! I completely disagree.
Try it: Yasmin agrees very strongly with Liam about summer. Which fits? (Absolutely! / I suppose so / I see it differently) Answer: Absolutely! — Absolutely! is strong agreement, which fits agreeing very strongly. I suppose so agrees only weakly, and I see it differently disagrees, so neither one is strong agreement.
Try it: Ira disagrees with her manager and wants to stay polite. Which fits? (I see it differently / You're wrong / No way!) Answer: I see it differently — I see it differently disagrees politely, which is what Ira needs with a manager. You're wrong and No way! are both too direct for work — save those for close friends.