The fact that other people are free to speak against you does not mean that you can't speak freely.
Free speech does not mean freedom from having your speech acts criticized (quite the opposite; it includes freedom of others to criticize your speech acts.) And, yes, it means that your speech acts may affect your ability to hold a job where you are one of the major public faces of an organization (such as its CEO) and are not capable of dealing with the PR resulting from the association of those speech acts with a public face of the corporation (the same as it would if you couldn't deal with any other PR issue affecting the corporation, even if it wasn't resulting from your speech acts.)
Free speech does not mean freedom from having your speech acts criticized (quite the opposite; it includes freedom of others to criticize your speech acts.) And, yes, it means that your speech acts may affect your ability to hold a job where you are one of the major public faces of an organization (such as its CEO) and are not capable of dealing with the PR resulting from the association of those speech acts with a public face of the corporation (the same as it would if you couldn't deal with any other PR issue affecting the corporation, even if it wasn't resulting from your speech acts.)