I believe that altruism is an illusion, if one defines altruism as an action that benefits someone else at the expense of the doer. An action which is apparently altruistic is done, at the very least, for the pleasure that it gives to the self.
Your definition of altruism strikes me as confusing. You seem to have at least two definitions of altruism. First, you plainly define "altruism as an action that benefits someone else at the expense of the doer" and call that an illusion. (Are you seriously suggesting that someone cannot do something that benefits another at ones own expense? That's absurd, isn't it?)
Second, you have a strongly implied definition of altruism as an action which is done for the benefit of another but with no benefit whatsoever to the doer. Do you see how that definition differs from your first definition?
So which is it? Is altruism to you an action that benefits someone else at the expense of the doer? Or, is altruism to you an action done for the benefit of another, but with no benefit to the doer?
In regards to your first definition, I would suggest the world is full of actions that benefit someone else at the expense of the doer. That is, I disagree with you that there are no altruistic acts in that sense of altruism. On the contrary, I think altruism is quite common in that sense of the word.
In regards to your second definition, I would suggest that defining altruism as an action done for the benefit of another, but with no benefit to the doer, is extraordinarily problematic. For one thing, if you look hard enough for some "benefit to the doer" you will surely find one. But are any and all benefits meaningful? For another thing, the question soon becomes how do you decide when a "benefit to the doer" outweighs any disadvantages to the doer in the mind of the doer?
For instance: If Smith jumps into the river to save Jones from drowning, and thus obtains some warm and fuzzy feelings for himself, how do you determine that Smith values those warm and fuzzy feelings so much that he thinks they outweigh the risk he's exposed himself to in order to help Jones? Is it not possible that Smith would see those warm and fuzzy feelings as incidental to some other reason he had for rescuing Jones? Or what if Smith is annoyed with Jones for Jones getting himself into trouble and he (Smith) does not consider any warm and fuzzy feelings he might have to be adequate compensation for his feelings of annoyance? Under those and other circumstances, how would you determine that the doer is obtaining benefits for his altruistic actions that mean more to him than the risk he's put himself to or other feelings (such as annoyance) that he might harbor?