Because Bitcoin is made to limit itself to 21 million total coins, coin loss is greater than zero, and demand is increasing faster than coins are being produced, Bitcoin is pretty much doomed to be permanently deflationary. If I own Bitcoins, why would I be eager to spend them if I know that they pretty much constantly increase in value right now? What value does Bitcoin have if it's now being used as a currency because of this pressure to save them?
This seems like a strange sentiment. Why would I ever keep my savings in USD if I know it'll devalue over time? I think the easiest answer would be that USD is convenient (and required, if you're a US citizen, to pay taxes). You don't see me spending all of my USD because I know it will be worth less later, likewise, I haven't saved 100% of my Bitcoin simply by virtue of knowing that it will be worth more later.
The blockchain is ever growing in size. If Bitcoin is going to survive for decades, how do we address the issue of the blockchain size? If Bitcoin were suddenly the size of Visa, how would it manage transactions?
The rate of storage costs decreases far faster than the rate of blockchain storage increases. The Bitcoin Blockchain is still under two hundred gigabytes, which is nothing in terms of data storage in this day and age. Also, Bitcoin, as it currently exists, will never support Visa-level amounts of transactions. It simply isn't capable of doing so and the core developers don't seem intent on ever trying to change that.
If I want to make an anonymous purchase, how is Bitcoin better than cash in most cases?
Well first off I'd like to point out that Bitcoin is pseudo-anonymous, not anonymous. You can always view transactions between addresses, so if you find out Person A owns Address A, you can rather easily start tying together what their payment history is like. If you want to use a Bitcoin-like system that is fully anonymous, then I'd suggest using Zcash or Monero, both of which have obfuscated blockchain histories that make watching transactions difficult (or even impossible in many cases).
SexWarrior touched on a few issues with cash, but I think an important one is that carrying large volumes of cash across borders is illegal or requires declaration in most countries (where 'large volume' is usually defined as $10,000 or greater). You also avoid things like losing whatever is carrying your cash or having it stolen out of luggage. Bitcoin as a cash substitute is much more secure from theft, though it certainly isn't immune from being stolen.