Why do people exercise call options early? If the price of the stock rises above the exercise price, the profit from selling the option would be greater than the profit from exercising the option and then selling the stock. If the price falls below the exercise price, there is no point from exercising the call option. So why do people do it at all?
Some people exercise a call to acquire a stock that they want to own. Some misguidedly exercise a call because they want to capture a pending dividend, thinking that the dividend is free money.
If the call has any time premium remaining, it makes more sense to sell it to close because doing so will incur less frictional costs. One transaction and you're done. If you exercise the call, you'll have two commissions - buy the stock via exercise and then sell it to close - unless your broker does not charge for assignment and exercise.
When calls get deep in-the-money, they often trade below parity. If you sell at the bid, you will take a haircut. For example:
XYZ is $10 and you buy a July $10 call for 50 cents. Just before expiration, XYZ rises to $14 and the B/A of the call is $3.80 x $4.20. The intrinsic value is $4 ($14 - $10) but the market maker is only offering $3.80 and that is a 20 cent haircut.
If you chose not to take the haircut, you could place a STC order for a higher price than $3.80. Maybe another trader comes along and you get 5, 10, 15 cents of price improvement but there is no incentive for the market maker or anyone else to give you the full $4. While waiting for a better fill, XYZ could drop in price and you would give back some of your $3.50 gain.
If you sell your call for $3.80, the market maker will immediately do a Discount Arbitrage. He'll exercise the call to buy 100 shares of XYZ at $10 and simultaneously sell 100 shares for $14, netting a 20 cent profit ( - $3.80 - $10.00 + $14.00).
If you have the funds in your account, you can do this exercise to close for yourself, avoiding the haircut.
Why do people exercise call options early?
I assume you are talking about American-style options that can be exercised anytime till expiry.
Say one has purchased a call option of buying 100 shares of ABC at $10 ea expiring in 1 month. The price (or the premium) paid is $50 total.
After a week the stock has gone up to $14. One believes this is the peak for the stock, and it may start going down. Thus it makes sense to exercise the option and buy @ $10 and immediately sell @ $14, making a profit of $400 - the $50 premium.
Instead of exercising the option, one could also sell the call option at this point in time. This would depend on how much the market is willing to pay for the specific option. If it is giving the same profit or more, it would make sense to sell the call option instead of exercising it.
If the intent is to buy the shares and hold and not pay more than $10 while anticipating the stock will fall, then the investor will hold the option till expiry and, if the price is above $10, exercise the option or else allow it to lapse and purchase the stock from market at the lower price of, say, $8. If the price is near enough like Ben Voigt mentioned in the comments, he may still exercise the option to save on commission.
At times, there could be tax considerations.
Aside from minimizing transaction costs, there is another situation when a call option should definitely be exercised early: when capturing an upcoming dividend is worth more than the time value sacrificed, as explained here.
Bob Baerker's answer mentions exercise before a dividend, but as a "misguided" attempt at "free money". Indeed it is not free money, but if one fails to exercise, one may be giving free money to the option writer. Some people deliberately write in-the-money calls with upcoming dividends in case some holders forget to exercise when it's optimal. This rarely works because the vast majority of contracts are held by savvy traders. In this situation, virtually all these options disappear through exercise, and then the next day (ex-dividend) a "new" call effectively starts trading, with the same name and terms, at a lower price, because the underlying dropped by the dividend.
In summary, early exercise can make sense for calls that are sufficiently in-the-money.
EDIT: It is of course possible for a trader to sell the call just before the ex-dividend date instead of exercising it, and get roughly the same value. This decision would relate to transaction costs. However, just as at actual expiration of an in-the-money option, this is a game of "hot potato" where someone ultimately has to exercise it that day in order to get the value from it. The open interest will go essentially to zero. In these cases a call on a stock about to go ex-dividend can be considered "pseudo-expiring".