Like all other financial institutions, they can process only certain amount of withdrawals in a time frame, limited by their banking partners and so on. Currently their are under enormous pressure, as their competitor Binance has decided to dump very large amount of $2B FTT token they received as part of the exit from FTX equity round where they were a seed investor. This will put FTT price under pressure and people correlate this price with the integrity of FTX. Also, FTX associated entities have loans collateralised by FTT tokens, so if the collateral value falls too much the loans are liquidated. Based on the FTX user agreement, this should not have effect on user deposits, but might have negative effects on other FTX associated entities like Alameda the quant trading desk.
The fear is causing everyone to withdraw from FTX and this has then clogged their withdrawal capacity.
Generally, if Binance would not have been hostile, they could have dumped their FTT tokens with less effect on the markets. They chose not to do so and telegraphed their dump very openly. This does not reflect well on the crypto industry as general. We will find out very soon.
Note that this kind of issues do not happen on decentralised exchanges (DEXes) where any reserves are transparent and smart contract controlled.