The tone when using 'put it to somebody that...' affects how it's received. Be mindful of diplomacy. I put it to him gently that his performance could improve.
Pro Tip 2/3
Not for Arguments
Avoid using this phrase in heated arguments; it's better suited for calm, rational discussions. I would like to put it to you that there might be another solution to this problem.
Pro Tip 3/3
Emphasize Opinion
Use the phrase to present your perspective without asserting it as an undeniable fact. I would put it to you that our approach, while unconventional, could be very effective.