under the pretext of illness; using illness as an excuse
Fixed expression meaning to use illness as a pretext for avoiding something or doing something else. Often implies the illness is exaggerated or not the real reason.
He skipped the meeting under the pretext of being ill.
It's not good to take time off work using illness as an excuse.
The phrase combines 病気 (illness) with the verb 託ける (かこつける, 'to use as a pretext'). The exact historical derivation is uncertain, but the expression is a conventionalized collocation.