There is no one reason for why humans are using non-renewable resources like fossil fuels and nuclear fuels to generate energy. I'll write what I know about and others can do the same and from all the answers you'll be able to see complexity of the situation.
To begin with humankind has been burning things for energy for millennia. It's something we know a lot about. Burning coal, oil and gas is and extension of an old practice.
The first usage of renewable energy was around 5000 BC when people put sails on boats. The Persians used wind power to pump water and grind grain from 900 BC.
One key aspect about burning non-renewable resources is that it can be done anywhere and at any time: on good farming country, in a desert, on a mountain, in the tundra, away from a town and in the centre of town. It can be done day or night, summer or winter, irrespective of whether its wet, dry, hot or cold; except during extreme weather like hurricanes or natural disasters. Fossil fuels are very good sources of base load power. If a generator is not running at full capacity it can increase its power output when required very quickly and likewise can reduce its power very quickly when required. This sort of flexibility is not available with renewable energy sources.
Renewable energy sources are limited in where they can be utilized and when. Wind power requires windy locations and for the wind to be blowing at speed powerful enough to generate electricity but not too powerful to damage the equipment. There are some issues with placing wind farms near population centres. Solar energy can only be generated when the Sun is shining and it will be affected by cloud cover and anything else that may interfere with the Sun shining of the solar energy collector . Peak generating times for solar energy is generally from late morning to mid afternoon. If solar energy isn't stored while being generated it can't be used during the night.
Tidal power can only be generated when tides are going in or going out (only twice a day) and where the tides are strong enough.
Wave power ultimately relies on the wind and is variable in strength. Water wheels require fast flowing rivers and are limited in where they can be placed.
Hydro-electricity requires the construction of massive dams. During the construction phase a lot of fossil fuel is consumed in moving rock and making concrete for the dam. There is also an environment impact in disrupting rivers and ecosystems. Additionally, all dams used for hydro power silt-up over time, which either renders the dam unusable or the silt must be removed. The dams also rely on consistent rainfall of sufficient quantities to keep water levels at required capacities. Also not all rivers are suitable for damming and hydro-electricity generation. But once constructed, hydro electric generators provide an excellent source of base load power that can be turned on and off at will, provided there is enough water in the dam, without additional atmospheric pollution.
Occasionally, people have used wind turbines to power pumps to pump some of the discharge water from a hydro-electric dam back into the dam. Solar photo-voltaic cells can be used for this as well.
Geothermal electricity can only be utilized when geothermal conditions are favorable: hot rocks near the surface of the Earth or in volcanically active regions where steam and hot rock are near the Earth's surface.
The generation of geothermal power from non-volcanic sources has been tried in Australia since the 1990s but it still requires a lot of money for development. Currently, only pilot plants have been made.
Non-renewable energy power stations can be built close to where the energy will be consumed which reduces the cost of electricity transmission, power lines and pylons, and it also reduces transmission energy losses by having short transmission lines. They are also relatively compact in size.
Renewable energy power stations tend to require large amounts of land: wind farms and solar generating sites. They also tend to be built to maximize the energy source and generally are located far from where the energy will be utilized. This requires longer transmission lines and increases the cost and the energy losses.
One of the main factors inhibiting the construction of renewable energy generating sites is the cost. Currently, in most parts of the world energy derived from fossil fuels is much cheaper than that of renewable energy.
The other thing that helps fossil fuels compared to renewables is that fossil fuels are considered sources of high quality energy; a lot of energy produced from a small quantity of material. Renewables are generally regarded as sources of low quality energy because their sources, like the Sun provide low amounts of energy. "Most people around the world live in areas with insolation levels of 150 to 300 watt per square meter or 3.5 to 7.0 kWh/m2 per day". Depending on the type of coal burned, energy from coal varies between 29 MJ/kg to 35 MJ/kg. This is equivalent to 7.7 kWh/kg to 9.7 kWh/kg. A lot a coal can be burned in a 24 hour day providing a lot energy.
The energy produced by natural gas is 439 MJ/m3, or 10.8 kWh/m3, which is even higher than that from coal. Uranium 235 can produce 24 million kWh/kg, which is 3.4 million times more energy than a photovoltaic cell, 1 metre square, can produce during one bright sunny day on Earth.
When it comes to using energy for transport, fossil fuels still give us the most flexibility and lowest cost options. Battery powered cars have a maximum range of approximately 300 km on a fully charged battery, which may be fine for driving around town but is not an option for long distance driving.
Buses in towns could revert to using overhead trolley wires, similar to what electric locomotives use, but from personal experience decades ago, they can cause traffic congestion when one or more such buses is waiting on another such bus to take or discharge passengers and all the buses must use the same trolley wire.
Hydrogen fuel cells can be used, but they are expensive and obtaining the hydrogen by splitting water generally requires the use of electricity. Also being highly explosive, hydrogen requires special safety measures and special thick walled tanks for storage.