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I also found this (even less pleasant) site http://www.milkproduction.com/Library/article_series/bovine_biology/35_Mammary_gland.htm which says

"If a heifer continues to cycle and is not bred, the...

Well, I wonder if the cow had had a calf at some point and your dad doesn't know or remember about that (maybe the calf was removed before your dad saw it, for example).

I believe that once a cow...

This (not very pleasant, you've been warned) article suggests it only happens if the heifer has some hormonal abnormality, or if they're given hormones artificially...