Because they have boundary issues. They are weak people who seek to control or to rescue others because they are avoiding healing their own wounds. Healthy strong people wouldn't care if you didn't take your advice and would not give unsolicited advice, either.
If it is on EP - it is probably because they believe they have the answer to your situation and want to save you from making a mistake.
If it is a professional - maybe it is because it is their job to give good advice... plus the above.
You have the right to not take the advice, but if what you are currently doing is not working - then I would look at trying another option.
It hurts their EGO'S and makes them feel inadequate.
How we give advice is important it should be communicated in a respectful manner is the advice being given correct also needs to be examined? If we accept the advice is just then it is unfortunately the stubborn ego at fault we "hate to admit we are wrong" line.
S/he might falsely thought that her/his advice is perfect for all people. If s/he felt offended, that would be a narural consequence. The problem is why we feel offended!
Who knows. Did they offer the advice themselves or was it after you asked them for it. Ah well, either way people have got to realize that if they haven't been published or if they have not been endorsed by Oprah, they have not officially arrived yet.
They must feel their advice is the way to go I guess...
Did they actually come back and tell you... Im offended you didn't chose my advice?