So you are asking if you buy a call option for a stock whose price is currently $50 but the call allows you to pay $40 for it, can you make a profit if the price falls?
It is theoretically possible but impractical. If the stock price is currently $50, then the call seller should charge at least $10 for a call at $40. If the stock goes down in price but stays above $40, you can exercise the call. But you will have lost money overall if you paid $11 for a call at $40 if the price is now $45. You've paid $51 for something that is currently valued at $45. It still may make sense to exercise the call, as the $11 is lost at this point. You might as well get back $5 if you can.
If you expect the stock to fall, you should sell a call at $40 for $11 (assuming that's the market clearing price). Then if the stock goes below $40, you make $11. If the stock goes down to $45, you make $11 + $40 - $45 = $6. You only lose money if the stock prices goes to $51 or higher.
It is theoretically possible that you could buy a call at $40 for less than $5 when the stock price is $50. But as a practical matter, it is unlikely. You could simply execute the call immediately at $40 and sell it for $50, making at least $5. So why would anyone sell that call?
Another reason to think that buying a call is a long position, is that it becomes more profitable as the stock price increases. And less valuable as the stock price decreases, until the stock reaches the price of the call.
Now, if you happen to find a stock at $20 and buy a call at $40 for $1, you might eventually profit after a downturn. The price could go up to $60 and then drop to $50. You exercise at that point, buying for $40. You sell for $50, making a $9 profit. But you would have been better off selling at $60. You made a profit, but not as much of one as you could have made if the stock didn't fall.
In general, you can't ignore the cost of the option. Until you purchase or sell the option, the cost is part of the prospective profit or loss. Once you've bought, then you care whether it is in-the-money or not rather than whether it is profitable. But you can't buy calls for a large premium, exercise them in-the-money, and be guaranteed of making a profit. You will lose money on in-the-money options whenever the option cost more than the amount you were in-the-money.
TL;DR: Buying a call (or selling a put) is a long position because it is more valuable as the stock price increases. Selling a call or buying a put is a short position because either becomes more valuable as the stock price decreases.