be bad at; not be comfortable withが marks the activity or thing that is difficult or unpleasant. The で connects to a following explanation or reason, and in casual speech it can leave the sentence unfinished, as in 「犬が苦手でね」 meaning “I’m not good with dogs, you know.”
JA: 私は人前で話すのが苦手で、いつも緊張してしまいます。
EN: I'm not good at speaking in front of people, so I always get nervous.