She was a genuinely radical intellectual in the sense that she took the generally accepted principles of her time to their logical conclusion in one big leap.
The principle she took to a radical conclusion was this: that our sex (i.e. the fact of being a man or a woman) should be made not to matter.
There are large numbers of liberals who support some version of this principle. It flows from a belief that the overriding good in life is freedom defined as individual autonomy. If you think that an autonomous, self-determining life is what counts, then you'll see whatever is predetermined as being an impediment to be overcome. Given that sex distinctions are predetermined, it follows logically that liberals will want to make such distinctions not matter.
Where Shulamith Firestone differed from much of the liberal left was this. Left liberals usually argue that sex distinctions are social constructs and therefore can be socially deconstructed. Firestone however accepted that sex distinctions are based on real biological differences. She therefore concluded that nature had to be overcome if sex distinctions were to be abolished.
...the end goal of feminist revolution must be...not just the elimination of male privilege but of the sex distinction itself: genital differences between human beings would no longer matter culturally....reproduction of the species by one sex for the benefit of both would be replaced by (at least the option of) artificial reproduction: children would born to both sexes equally, or independently of either...
Firestone wanted to free women from the tyranny of being biologically female. She saw it as a tyranny because she believed in autonomy as the great good in life; she did not think that a woman could be autonomously independent when she was subject to pregnancy and then the nuture of children. She thought that this inevitably made women dependent on men for support.
And so Firestone took a very hostile view toward pregnancy; toward women looking after dependent children; and toward the act of sex which led to these things. She wanted to bust up the biological family and replace it with artificial procreation.
These views did not create a happy life for Firestone. In the 1980s she suffered from mental illness and she died alone, not being discovered for a week after her death.
Her fault was not to examine the underlying principles she was working with closely enough. She did not see motherhood, or family, or marital love as goods in themselves, goods which were not always to be subordinated to the pursuit of a radical, individualistic autonomy. She operated with a reductionist account of the human good, one which distorted her view of what might be valued in life, and so she failed to see politics as an application of wisdom and experience to the ordering and weighing of a range of possible goods.