If shares bought at less than say $3 were sold at $3 there may...

If shares bought at less than say $3 were sold at $3 there may well be capital gains tax and brokerage to pay for that sale. That reduces the amount of funds made from the $3 sale so less available with to buy back in than the proceeds from the $3 sale.

Thus not always (rarely) the case that a sale at $3 and purchase at $1.50 means a doubling of the number of shares held.

The lower the price at which the original shares were bought and the higher the other income against which the capital gain is taxed, the further down the buy-back-in share price needs to be to result in holding more shares than one started with.

Just pointing out, it may not be as simple as saying someone could have/should have sold and bought back in to “make a profit” … all depends on each investor’s own circumstances.