Employee stock options: why is the total number of shares a secret?

You seem not to understand how stock option work, which makes it difficult to answer your question.

Here is quick overview:.

1. Stock options granted to an employee as part of their compensation and/or hiring bonus.
2. Stock options give the owner the right to buy stock in the future at a specific price, called "the strike price" which is typically the fair market value at time of grant
3. Initially stock options are worthless: in order for them to create value the share price needs to go up.
4. Stock options "vest" over time, i.e. you can only exercise after a waiting period (typically 4 years with partial vesting after one year).
5. The employee doesn't have to pay anything until they choose to exercise any options
6. Typically you don't exercise unless there is a way to actual sell the shares. That's easiest if the share are publicly traded, but there are other mechanisms as well.
7. Exercising option and selling shares can have very complicated tax implications: it's strongly recommended that you discuss this with a financial advisor first. Some people in the US have been bankrupted by this!

why is the total number of shares a secret?

Because it doesn't matter. You are not getting "a percentage of the company" you are getting the right to buy shares for a certain price in the future.

In order to valuate the stock options you need to guestimate what the stock price in the future will be. For a non-public company the share price is typically set by the board of directors in regulars intervals, so you can track this and see where it goes. The total number of outstanding shares simply isn't relevant for the value of your options.

Because they don't want other people to know. There's no incentive for the company to share this information with you or anybody else. Why would they want your friend to know how much (or little) of the company your they are getting? They also don't want this information getting into the wild for the world to know.

But it DOES matter, and your friend should press for this. However, unless they are a particularly desirable or high-level candidate, they are unlikely to be successful.

Your friend might still choose to join the company even if they don't have all the information, but it's a bigger gamble and they need to know that they might not really have that much value in the options and consider the offer accordingly.

I've joined companies without knowing what fraction of the company my options represented and not regretted it. It is what it is.

Also, they should be very clear what the vesting schedule and triggers are. If they leave after 18 months, while the company is still private, do they keep any of the options? VERY important question! It is trendy these days (for tax reasons) for vesting to require both time AND a "liquidity event" (going public, getting acquired, etc). So your friend can get trapped where they have $1M in unvested options that they don't want to leave behind ("golden handcuffs"), but those options may NEVER vest.