Looks from the image of you lifting the damaged comb is that you started your inspection on the #2 frame. It is good practice to always draw the #1 comb first, and then use the expanded open space to pull subsequent comb without returning the #1 to the hive. The real risk of not doing this practice is "rolling the queen". You damage the queen by crushing her when lifting comb with no additional space.
I pry all 10 frames away from the box side by inserting the frame tool and levering sideways. This breaks any burr comb on the #1 away from the box side and opens up a bit of extra space.
I then pry the #1 away from #2 and back towards the side, centering it in its frame space. Then you can lift the #1 without "tearing" comb. Queens are virtually never on #1.
Subsequent frames are lifted by levering into the open space to free them up. You can replace these subsequent combs, to the side of the hive, no need to keep them out.
In very heavily burred or otherwise tight hives you can pry from both sides to get a bit to get some space, observe where the natural break is, and lift 2 or 3 combs as a unit, only separating them after you have them free of the hive.
"Rolling the queen" is one of the primary reasons new keepers seem to lose queen-right so frequently.