Term for particularizing someone's behavior in a discussion where they aim at avoiding to be blamed for having a double standard
Solution 1:
To explain away a phrasal verb: TFD
to dismiss or minimize the significance of (something) by means of an explanation or excuse
As in:
There is no way to explain away my carelessness.
Solution 2:
One of the senses of rationalise / rationalising covers this, though it is broader in scope:
rationalise ['BrE' spelling] verb ...
1 Attempt to explain or justify (behaviour or an attitude) with logical reasons, even if these are not appropriate.
{ODO} (ODO does not mention the intransitive usage; M-W does.)