I like James Naughtie and John Humphrys. With regard to their apparent "rudeness" when interviewing these two are seasoned professionals.
One or other usually does the the main serious interview post 8am on the Today program. This is probably the most important slot of the day on any BBC news program.
They are up against experienced politicians etc, who themselves have themselves been well trained in the art of avoiding interviewers potentially difficult and embarrasing questions by deflecting the issues and doing what ever they need to try and avoid any direct questions.
This is a game like a tennis match you cannot afford to let you opponent get away with anything.
I am not at all surprised then, that these interviewers do not want to let their subjects get away with not answering and so they keep pushing for an answer that is clearly being avoided. Do not feel sorry for thes politicians here they know exactly what they are doing.
The all female team of Mishal Hussein and Sarah Montague can be similarly persistant in their questioning.
Hilda W I did not know that about Robert Pestons stammer, but now you mention it I can see how it might affect his slightly strange speech patterns.
I also think Robert Peston puts a bit of excitement into business and finance. Well done him.