Ted Cruz’s strange gambit of announcing on Wednesday afternoon that Carly Fiorina will be his vice presidential running mate, done while his own bid for the presidential nomination is still a long shot, reeks of desperation. But there’s a certain logic to it. After all, Donald Trump is extremely unpopular with women, including Republican women. And further down the line, Hillary Clinton is the presumptive Democratic nominee. So Fiorina as running mate is a way to show that Cruz can outflank both Trump and Clinton (whom Cruz repeatedly linked together in his speech making the announcement). Fiorina can, theoretically at least, both call attention to Trump’s sexism and provide a conservative alternative to Clinton’s version of feminism. Fiorina’s own presidential bid was short-lived, but she enjoys a broad popularity in Republican circles, as shown by the warm reception she received at the Indianapolis announcement event, where she did a much better job energizing the crowd than the man who still hopes to be at the top of ticket.

Yet Cruz, who has a sure instinct for the sensibilities of the GOP’s right wing, was also aware that a Fiorina pick raises certain delicate problems because of conservative unease with successful women. After all, the GOP is the party of gender traditionalism, and that thread is especially strong among the evangelical Christians who are the core supporters of Cruz’s presidential bid.

That’s why both Cruz and Fiorina played a curious double game at the announcement: They tried to be both feminist and anti-feminist at the same time, arguing that Fiorina is strong enough to stand up to Trump while also insisting that she possesses maternal instincts becoming of her gender.

In his characteristically long-winded speech introducing Fiorina, framed strategically for TV cameras by an all-female audience standing and cheering behind him, Cruz called attention to Trump’s sexism, reminding listeners that the real-estate mogul had insulted Fiorina’s appearance with his “look at that face” comment to Rolling Stone.

But Cruz was also careful to make the point that while Fiorina is a strong woman, she still upholds traditional gender divisions. Cruz said that Fiorina had befriended him and his wife (emphasizing Fiorina’s interpersonal rather than political skills), and that Fiorina had become especially friendly with the two Cruz daughters, Caroline and Catherine. Fiorina, Cruz said, has “a very impressive fluency with heart and smiley faced emoticons,” useful talents when texting young girls.

The implications were hard to miss: Fiorina might be a successful career woman but she is still maternal and (unlike, say, Hillary Clinton) fundamentally non-threatening. Fiorina echoed that same double message during her speech, which forcefully hit all the Cruz campaign talking points but also had a strange interlude where, in an instantly legendary moment of cringe-inducement, she sang a song she said she composed for the Cruz girls:

I know two girls I just adore
I’m so happy I can see them more
Cause we travel on the bus all day
We get to play

To some degree, Fiorina is playing the same game that Sarah Palin did as John McCain’s running mate in 2008: trying to be a gender pioneer while also assuaging the worries of social conservatives. But this curious mixture of feminism and anti-feminism takes on a sharper edge in the age of Trump and Clinton. Fiorina and Cruz are trying to separate themselves from both the toxic masculinity of Trump and the embrace of liberal feminism by Clinton. Part of the political problem they might face is that no such middle ground exists. With Trump and Clinton offering starkly competing gender politics, there’s no longer a constituency for the “she’s strong, but she’s a lady” compromise offered by Cruz and Fiorina. Indeed, it might be that there was never much of a market for such a clearly conflicted position to begin with.