Weak Point, Poor At, Not Very Good At, Bad At
Noun and な adjective
にがて
ちんもくが苦手です。
Silence is hard to deal with.
「コウイチが苦手なことって何ですか？」「ぼくは歌が苦手です。」
"What is your weak point, Koichi?" "I'm not good at singing."
俺とお前は昔は切っても切れない仲だっただろ。でもさ、 ほら、今は昔とは違うというか何というか、えっと…正直いって、お前のこと苦手なんだよ。
You and I used to be inseparable, but you know, now it’s like… things are different. Honestly, I feel uncomfortable with you.
A "suffering hand" is a little misleading. Think more in terms of the words 苦い (bitter) and 手 (person... remember how that happens sometimes?). Now think of this word like you're bitter about having to work with someone. Why? Because they are extremely hard to deal with.
The reading is that of 苦い (にがい) plus regular old 手 (て). Remember, this is your bitter person, the person who's "hard to deal with." So, it uses the strange にがい reading.