Why can't i STAKE my BTC?
Because BTC is not a shitcoin.
My understanding of proof of work is that basically (miners/CPUs provide power to write transactions on the blockchain)
In PoW the computing power and the fact that by consensus rules we follow the chain with the most work is used to ensure reversing the blocks is so costly that it can be considered impossible. That way we ensure immutability of the blockchain.
whereas Proof of stake (is when we hold a certain currency and lock it into the systemso liquidity increases).
Liquidity doesn't change whether or not you hold or stake a coin.
Basically, in early days when developers were more interested in improving the technology, someone came up with the idea that a new algorithm could be introduced where nodes process transactions and get paid for doing so. Hence Proof of Stake came to life.
But this was a very flawed approach for many reasons. From different attack vectors to the economical design flaws (you get paid for having money!).
Also why is it that only some coins can be staked?
Depends on the coin. Early coins were as I explained above, exploring changes in Bitcoin technology. Newer coins are mainly using PoS or planning to switch to PoS so that they can make sure their coin is going to die when the miners abandon it due to high difficulty or price dump.
In some cases like ETH they are making the switch to
also ensure their own revenue since they hold tens of millions of ether and in PoS you get paid to own that coin!!!
What are the conditions for a coin to be eligible to be staked?
The algorithm has to allow that.