A trope is something that's been explored in so many books or other forms of entertainment that it has slipped into the collective unconsciousness. They can be useful storytelling tools, but if you let the tropes do the heavy lifting you end up with cliched characters or a predictable plot people have read a dozen times before.
You can subvert the trope by flipping it on its head, but it's not a panacea. Making all the women in your story gruff and men emotional only means you've made your cliches swap bodies. Same product, different packaging.
What to do, then? Well, you've already provided a partial answer to your own question by saying that you want your characters to grow. If you portray your characters as if they could be actual people, if you make their struggles and problems faced relatable, if you can make them emotionally resonate with your readers, your readers will care little whether the character is male or female.
A grown woman who bawls her eyes out because she stepped on a ladybug is a ridiculous stereotype. A grown man who bawls his eyes out because he stepped on a ladybug is equally ridiculous. Neither are ridiculous if a week ago they had to bury their four year old daughter who died after her struggle with a terrible disease, and loved nothing more than to play in the meadow behind the house and catch ladybwuhgs with a butterfly net.
Sometimes you don't even need to do all that much to make a character less of a stereotype. My favorite science fiction novel is Neuromancer. 846
Its male protagonist, <PERSON>, is an archetypical loner. He's a drug-addicted criminal who, for the first 250 pages of the book, shows about as much emotional reciprocation as a cardboard box. Very early on in the book he finds the dead body of <PERSON> (a person he once had feelings for) and just... acknowledges the fact.
Near the very end of the book he's sucked into cyberspace by the titular Neuromancer, and finds a simulated version of <PERSON>. He knows she's a fake, even tells <PERSON> this to his face. Yet in a blink-and-you-miss-it moment he hands Fake <PERSON> his jacket. In case the collection of ones and zeros gets cold. That little scene does a lot to suggest there's more to <PERSON> than the stereotype suggests. 295