You're about to say something the other person may not like. A short phrase first warns them and softens the hit.
Way 1 · best default
You show you know it's awkward, then ask or say it anyway. Great with strangers.
Examples
I don't want to be rude, but could you turn your music down a bit?
I don't want to be rude, but I think that's my seat.
In a conversation
A: Sorry, is something wrong?
B: I don't want to be rude, but I think you've taken my coffee.
Way 2 · between friends
Casual and often jokey. Only with people who know you like them.
Examples
No offence, but your cooking has got a lot better.
No offence, but that jacket is very nineties.
Way 3 · unwelcome truth
You're sorry the truth is what it is. Good for bad news you both wish wasn't true.
Examples
I hate to say it, but that place has really gone downhill.
I hate to say it, but I think we're lost.
In a conversation
A: Shall we go back to that Italian place on Friday?
B: I hate to say it, but it's not as good as it was.
Way 4 · honest opinion
You're giving your real opinion, even if it's not what they hoped for.
Examples
To be honest, I think the report needs a bit more work.
To be honest, I preferred the first version.
Common mistake
Not: Frankly speaking, your report is bad.
Say: To be honest, I think the report needs some work.
"Frankly speaking" sounds like a textbook and quite harsh. "To be honest" plus "I think" is softer.
Way 5 · personal remark
For a personal comment to someone you don't know very well. Careful and respectful.
Examples
If you don't mind me saying, you look exhausted. Take a break.
If you don't mind me saying, the second slide is a bit busy.
Way 6 · formal challenge
Before you challenge someone senior. Formal, and in an argument it can sound cold.
Examples
With all due respect, those numbers are from last year.
With all due respect, I don't think the team was consulted.
In a conversation
A: The whole team agreed to this months ago.
B: With all due respect, the team was never asked.
Common mistake
Not: With all respect, I disagree.
Say: With all due respect, I disagree.
It's a fixed phrase: "with all due respect". Leaving out "due" sounds wrong to native ears.
Read the moment, then choose the way that fits it best.
Pick one and practise it in a real conversation. Save the ones you want to remember.