Because it means you have a chest infection and apart from the risk of triggering an asthma attack if you are vulnerable it does not make sense to try and train when your lungs are affected.
Puffing bertie, even though they say you can run with a cold if its only in the head I wouldn't do a hard training session with a cold, if you are going out keep it easy/steady and prehaps a shorter session.
A cold below your neck will affect your breathing and so best not to run.
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A chest cold includes the whole respiratory tract and infection could spread into the lungs... as my Granny used to say 'it will give you pneumonia'.
I've found I can easily run with a headcold and often it actually clears the pathways.
..anything more of a cold and you'll end up with a sore throat, cough or even worse.
A cold below your neck will affect your breathing and so best not to run.