cannot suppress one's emotions; cannot help but feel
Used with emotion nouns like 感謝, 同情, 喜び, 悲しみ, often in the pattern ～に堪えない to express an overwhelming feeling one cannot hold back.
See also: こらえる
I am overwhelmed with gratitude for everyone's kindness.
Hearing his unfortunate story, I couldn't help but feel sympathy.
cannot bear the responsibility; unable to cope with one's duties
Used with nouns like 責任, 重責, 任務, often in the pattern ～に堪えない to express that the responsibility is too heavy to handle.
He resigned, saying he could not bear the heavy responsibility.
I am not equal to such an important role.
Negative form of the verb 堪える (to bear, to endure). The expression ～に堪えない literally means 'cannot bear ~', and has developed idiomatic uses for overwhelming emotions and heavy responsibilities.