Humidity is not enough
Even when humidity is nearing 100% saturation, you can still start a fire. What does make fires hard to start is rain... lots and lots of rain. When it rains, would be firewood becomes nearly impossible to light using primitive means for the next 1-5 days. Also, it has to be rain, not snow. The moisture from snow does not seep into the wood; so, if you have snow capped mountains, your people could just go up to the mountains to collect firewood. So for your world to act like you want you need the whole planet to be constantly hammered by liquid rain. This is nearly impossible on a world that looks like Earth; so, your planet will need nearly all of its land mass isolated to the tropical zone with short mountains and a fairly small axial tilt to prevent your people from experiencing colder-drier seasons, rain shadows, or snow capped mountains where they could make fire.
Without fire, you loose out on several really important early inventions
1- Metallurgy: Without metal tools, you are stuck in the stone age. Without metal tools, agriculture becomes so labor intensive that you can not reliably sustain yourself off of farming it in most regions. If you can not stop to farm, you can't build a very large or advanced civilization.
2- Ceramics: This is not just pots and cups, but bricks to. Your people will still be able to make wicker baskets for holding dry goods and use hollow gourds to store liquids, but lack of bricks makes creating permanent structures in tropical areas where exposed stone may be rare virtually impossible.
3- Mortar/Concrete: The active ingredient in early forms of mortal and cement is quicklime which you need to scorch limestone to get. Between this and lack of bricks, making large permanent structures becomes a lot harder. Add to this a lack of metal tools, and shaping stone into stable stack able bricks is nearly impossible anywhere. Stone with mud mortar or compressed earth construction will make mostly permanent buildings in dry areas, but since you don't have dry areas, you are basically stuck living in building made out of wood, leaves, and grasses.
4- Fire-hardened wood: fire is often used as a way of hardening wood for various purposes. Especially since you are in a humid environment, this means your spears, axes, and hammers will break more easily, and bows might not even be possible to make.
5- Hide-glue & tree resin glue: Not only were these early adhesives the only kinds of glues available throughout most of history, but they were also important water proofing agents. If you can't boil hide or tree sap, you can't make glue; so, this means you can't make leak proofed water skins, you can't make composite bows and even adding wooden handles or shafts to stone tool heads becomes harder since the bindings were often hardened and secured with a layer of glue.
6- Fire-boaring: Another common way to fix a stone head to a wooden handle involves using fire to "drill out" the hole you need. Without fire boaring or glue, the only way you have left to attach stone to wood is by tieing it in place which is not particularly reliable.
7- Leather, raw hides, and furs: Animal pelts that are not fully dried (usually by sun baking or smoking) will begin to rot within a few days.
The end result here is that most people would remain nomadic. Nomadic civilizations are inherently size limited because they can only feed people based on the natural densities of available food sources. This size constraint also means you will never have enough minds in one place to really advance very far. The few places you could farm well enough using only wooden tools would be impossible to fortify well without shapeable stone or brick walls. When you look at the late stone age, early towns that did not have strong walls were routinely overrun by nomads; so, without the ability to make these stone walls, any attempts at early sedentary civilizations would tend to fail.
In short, not only are you stuck in the stone age, but the early stone age at that.
Now let's look at the lucky civilization that can start a fire
In our own history, various estimates indicate that it took somewhere between ~300,000 and ~2 million years to get from the discovery of fire to cook and stay warm to the use of fire as the foundation for all these other important technologies. Some of that time may have been evolution happening requiring our brains to be capable of becoming creative enough to make these leaps forwards. However, with so few humans in your setting being able to make fire, not only is accidentally finding better uses for fire harder, but you also take away most of the environmental pressure that made human creativity so selectively fit in the first place. In our own history, the hominids who could find the most uses for fire pushed out the other races, but on your world, the faster, stronger, healthier hominids will win out nearly every time; so, even those few places with enough pressure to push intelligence forward will likely see so much diffusion into the dumber surrounding populations that they will never get very far.
The only way I can see to solve for this is to isolate a population. Perhaps there is a large island away from the tropical zone which is mostly dryer than the rest of the world and cut off from moister areas. In this case fire using humans could evolve separately from the fire-less ones. Then when they go to expand to the rest of the world, they could bring things with them like metal tools and tinder kits. By bringing tender kits, and metal tools, they could craft stoves that would isolate the fire from moisture, and the tender kits would allow them to start fires on damp wood. Once they have the fires going, they could then make more tender kits, more tools, more bricks, and all the other stuff that our own ancestors were able to spread to the rest of the world.
One last thought
Even all these ideas to make your setting works may all be in vain if your humans are cleaver enough to simply prepare dry storage areas for thier wood. Using only stone tools, one can make an elevated covered structure that would allow wood to dry out enough to use, even in a place that rains all the time.