After the block-halving, the supply will reduce which will lead to the price increase, and demand will increase due to attractive prices increased with the help of low supply.
I don't see that it will cause some damage to the mining pools after block-halving but I think only miners who will suffer due to halved rewards they get and due to operational cost.
Probably he referred the miners by using the term "mining pool".
Unlike you mentioned, price increase will not happen immediately following the halving. That is where the point, OP is referring. Until, prices turn profitable, definitely miners will suffer which may lead to less number of miners in a mining pool; and probably OP is mentioning that situation as a damage
![Grin](https://bitcointalk.org/Smileys/default/grin.gif)
.
The time gap between halving and BTC prices to become profitable for miners must be a struggling period for both miners and common bitcoiners. Yes, we are the people who suffer because of 100x more tx fees than usual. People who make 1 or 2 transaction per month may not suffer but the others. So, halvings do damage not only the miners but also the frequent BTC transactor. The only consoling thing is, expectation of higher value for BTC in near future as past halving have done that so why not this time as well
![Smiley](https://bitcointalk.org/Smileys/default/smiley.gif)
.