That may be true in many companies, but venture capital funded companies almost always have something called a "Voting Agreement". I pulled a random one from my folder of docs, it is below. The upshot, if you are not used to reading these, is that all of the shareholders signed an agreement that says they will vote their shares to elect certain directors. In the absence of an agreement like this you are right, the board could fire the CEO but the majority shareholder could fire the board. But, again, every equity round from a VC that I have seen in the last 25 years (and, I assume, longer, but that's as far back as my personal knowledge goes) has a Voting Agreement in some shape or form.
Actual text from a Voting Agreement:
"NOW, THEREFORE, the parties agree as follows:
1. Voting Provisions Regarding Board of Directors.
1.1 Board Composition. Each Stockholder agrees to vote, or cause to be voted, all securities of the Company the holders of which are entitled to vote for members of the Board, including without limitation, all shares of Common Stock, Series A Preferred Stock, by whatever name called, now owned or subsequently acquired by a Stockholder, however acquired, whether through stock splits, stock dividends, reclassifications, recapitalizations, similar events or otherwise (“Shares”) owned by such Stockholder, or over which such Stockholder has voting control, from time to time and at all times, in whatever manner as shall be necessary to ensure that at each annual or special meeting of stockholders at which an election of directors is held or pursuant to any written consent of the stockholders, the following persons shall be elected to the Board:
(a) For so long as there remain outstanding not less than 200,000 shares of Series A Preferred Stock (subject to appropriate adjustment in the event of any stock dividend, stock split, combination or other similar recapitalization with respect to the Series A Preferred Stock), one (1) individual designated by the holders of a majority of the shares of Series A Preferred Stock then outstanding, which individual shall initially be Jerry Neumann (such director being the director defined as the Series A Directors in the Restated Certificate); and
(b) Two (2) individuals designated by the Key Holders who are at such time providing services to the Company as an officer, director, employee, consultant or advisor holding a majority of the Shares then held by such Key Holders (each such director being one of the directors defined as a Common Director in the Restated Certificate);"
That is how it works. The board has the power to fire the CEO in all companies that I know of. (I suppose you might be able to write the bylaws so this isn't true but I'm not sure; a corporate lawyer would know.) The best you can do is to have an employment contract that regulates how the firing happens (ie. do you get severance, accelerated options, longer option exercise times, COBRA, etc. if you are fired without "cause", with cause carefully defined.)
Removing you from the board itself is a different matter. But that's usually also explicitly covered: they don't put the founder in the "Common seat" they put the founder in the "CEO seat." That way, when you're fired as CEO you automatically lose your board seat.
Very few things in a VC-backed startup require a shareholder vote. Firing the CEO is not one of them (this is a board vote.) Electing directors to the board is not one of them (this is usually the subject of a voting agreement that ensures board representation by the VCs.)
Let's say the company raises money from VC1, who buys 20%, leaving you with 80%. The contracts add VC1 and an independent to the board, alongside you. Later the company raises money from VC2, who buys 20%, leaving VC1 with 16% and you with 64%. The contracts add VC2 to the board.
Now the board is VC1, VC2, an independent, and you. If the VCs can convince the independent director to vote with them, the board can fire you, even though you own 64% of the company.
Actual text from a Voting Agreement:
"NOW, THEREFORE, the parties agree as follows:
1. Voting Provisions Regarding Board of Directors.
1.1 Board Composition. Each Stockholder agrees to vote, or cause to be voted, all securities of the Company the holders of which are entitled to vote for members of the Board, including without limitation, all shares of Common Stock, Series A Preferred Stock, by whatever name called, now owned or subsequently acquired by a Stockholder, however acquired, whether through stock splits, stock dividends, reclassifications, recapitalizations, similar events or otherwise (“Shares”) owned by such Stockholder, or over which such Stockholder has voting control, from time to time and at all times, in whatever manner as shall be necessary to ensure that at each annual or special meeting of stockholders at which an election of directors is held or pursuant to any written consent of the stockholders, the following persons shall be elected to the Board:
(a) For so long as there remain outstanding not less than 200,000 shares of Series A Preferred Stock (subject to appropriate adjustment in the event of any stock dividend, stock split, combination or other similar recapitalization with respect to the Series A Preferred Stock), one (1) individual designated by the holders of a majority of the shares of Series A Preferred Stock then outstanding, which individual shall initially be Jerry Neumann (such director being the director defined as the Series A Directors in the Restated Certificate); and
(b) Two (2) individuals designated by the Key Holders who are at such time providing services to the Company as an officer, director, employee, consultant or advisor holding a majority of the Shares then held by such Key Holders (each such director being one of the directors defined as a Common Director in the Restated Certificate);"
etc. etc.