That's a weird way of putting it! As if you are suggesting that without a block subsidy, people won't be able to accumulate bitcoin! Which may be the reason for your follow up question.
It is too weird and unlogical if he actually thought like that but I think he meant something like: there will be very little bitcoins in future (new) supply in total supply of Bitcoin, and demand will be bigger with time. This leads to higher buying demand and price will move up, then Bitcoin price will be more expensive than now and in the past, according to supply and demand principle.
Hopefully it is his thought.
Trading bitcoin (and people accumulating it) takes place on the market and is unrelated to mining and its reward. People buy and sell bitcoin from and to each other on the market. Any coin you buy from an exchange today is many "hops" from a coinbase reward. Which means in the future without a block reward, the market should not change at all. People will still continue trading with each other with the coins they have.
Trading bitcoin is one of ways to increase your bitcoin amount but at the same time there is risk to lose your bitcoin especially if you trade with margin and futures. In the market, most traders lose money, lose bitcoin in trading, not get more and thinking like trading will help a trader to enrich his bitcoin portfolio is quite dangerous.
Only intelligent and experienced investors can take advantage of bad traders in the market in order to accumulate more bitcoin.