Borderline ad hominem is not a strong argument. But I'll try to respond.

First, note that any response will be necessarily shallow and inadequate. I don't know what your level of familiarity is with Nietzsche, but since you didn't know who Simone de Beauvoir is, I assume you know nothing of mid-20th century French existentialism (Sartre, Camus, de Beauvoir). My own understanding of Nietzsche is admittedly shallow, but still probably more nuanced than average. I've at least read some of his work, rather than just broadly-misunderstood pithy quotes like "God is dead".

And of course, I'm summarizing in an online comment, for an overtly hostile audience who obviously doesn't understand even the basics of half the equation. So this will probably fail.

Simone de Beauvoir's criticism of Nietzsche, in the context of The Ethics of Ambiguity, arises from her core premise, which is that our own freedom depends on the freedom of others, so we have an ethical obligation to advance the freedom of others in order to make our own freedom meaningful. Now, existentialists view suffering in a couple of different ways. First, there is suffering from constraints on our freedom. This is what older modernist philosophers like Nietzsche generally mean by suffering. Second, there is suffering from awareness of our freedom, which we find frightening. This idea really starts with Sartre's Being and Nothingness, and is a big part of the difference between existentialism and earlier philosophy.

Nietzsche was generally hostile to compassion, finding it indistinguishable from pity most of the time. He believed that freedom comes from overcoming adversity - by defeating constraints to our freedom through struggle. "That which does not kill me makes me stronger". So to help others achieve their own freedom is to risk pity, which is a useless emotion. Letting them overcome (or fail to overcome) their own adversity, without aid, is the best thing to do for others, and adversity is welcome and vital.

So de Beauvoir's criticism of this is that it leads to a situation where it is okay to harm others, to constrain their freedom for our own selfish desires. That's not Nietzsche's intent, but it's nonetheless the outcome. The fact that Nietzsche is so popular with fascists (which he would have found horrifying) lends credence to this point of view.

For more than this, the only answer I have is to read The Ethics of Ambiguity yourself. I highly recommend it. It's relatively short (under 200 pages) and quite beautiful, and very enlightening. It's the perfect companion piece to Sartre's Being and Nothingness, another brilliant and greatly misunderstood work.

A bit more here... de Beauvoir responds to the idea of fear of freedom with a list of personality types that are responses to our natural fear of freedom - the Sub-Man, the Serious Man, the Nihilist, the Adventurer, and others. Now, if you're still kicking back at me for daring to criticize Nietzsche, I'd suggest you're being a Serious Man. The Serious Man deals with fear of freedom by finding something external to himself to elevate to greater importance than himself. The Serious Man is extremely hostile to any perceived criticism of the thing he's serious about - his religion, his political ideology, his nationality, whatever. It's easy to be Serious about Nietzsche, but it's a mistake. It denies you the freedom to understand Nietzsche better, if you can't take the idea that he's being criticized without attacking the critic.