Difficult to discard a photo with 〜がたい
Grammar Explanation: Difficult to do with 〜がたい

Inui’s class is gathering photos of couples for a school festival contest. Another couple comes to join in.
- 乾:
- 「どっちの画像プリントします?」
- “Which image should I print?”
- 彼女:
- 「えーーー どうするー?」
- “Oh my gosh... What should we do?”
- 彼氏:
- 「どっちも捨てがたいねーーー」
- “Both are hard to abandon.”
The verb 捨てる means to discard or abandon. Because the couple has to select an image to print, the other image will be “thrown away” in the sense that it won’t be printed for the contest. In English, it’s more natural to say it’s different to choose between the two, while still retaining the same general meaning.