If you don't know where you want to go, then any map, trail, tactic, or maneuver is useless.
The same holds true in design and branding. If you don't know what emotions/values you want your logo, colors, language, website, or collateral to align with, it's unlikely you'll be satisfied. At the very least, you'll have no objective way of dictating right decisions from wrong decisions.
That's the point of strategy. Strategy gets you aligned. It points you in a direction. How you get there can take many forms, so long as it gets you to the destination.
Where do you want your brand to go?
The startup world is cut throat. It seems like there is always some kind of monstrous competitor lurking around the corner ready to devour your company. At least, this is what a scarcity mindset would reinforce.
The sad thing is that even if that monster is beaten there is another one ready to take its place. Concerns about competitors are like a hydra. Cut off one head and two more take its place.
What are we to do?
Walk past them. Don't engage. Your brand has one enemy and that is who it was yesterday. The bliss embedded within such a mindset is that whether you win or lose, it's all up to you.
In Genesis, the first sin recorded outside of the Garden of Eden is the murder of Abel by his brother Cain. Whether you believe the story to be historically accurate or not, there is a provocative truth to it. Cain had become extremely bitter and resentful of his brother, as Abel's offering to God was accepted and Cain's was rejected (due to his lack of reverence and thoughtfulness in the offering). These emotions boil to unrest as Cain wields a rock to bash in his brother's skull. He rids the world of his competition so that his own subpar efforts have nothing to aspire to.
What does this have to do with branding and being rebellious?
While competitive analysis and an understanding of the market is a good thing, comparing the shortcomings of your brand to others is a recipe for bitterness and resentment. If Cain had instead looked inward and been in competition with himself, he would have slain hi sown inadequacies instead of his brother.
Rebellious brands inherently take on a different mission from the rest of the world, and without a doubt there will be times when it seems like the competition will be doing it better.
Let them. Make friends with them and leave behind the scarcity mindset.
Focus on improving your brand, having a greater understanding of your faults, and figuring out how to be better than you were yesterday.