Why did it take so long for the Germans to develop the first tank model in World War I?

There is often problems with militaries having trouble adopting new tech that has little to do with actually building new technology. The German high command thoughts on war didn't include tanks and the way their government was set up dissenting opinions did not have much of a chance.

From a technical standpoint, all the major countries should have had tanks at the start of the war. There was no major technical hurdle in the way. It was even pretty common in the sci-fi literature of the time. Large earth-moving equipment had already been invented.

Most countries' militaries botched it just like Germany. In Britain the idea didn't exactly get much traction. Ignored by most of the government and stuck in a committee with limited access to resources. With the war stuck in trenches with lots of depth they had to design tanks specifically for defeating those trenches which added time. Then the tanks had to prove themselves at Cambria before large scale production orders.

Look at the numbers of the tanks Germany built. Even when they had to, they were just plain reluctant. It wasn't a issue of steel for they only built 20 tanks. They built a lot more battleships than tanks. The allies built thousands of tanks and were really expanding production when the war ended.

Really, the development of the tank just shows how some ideas rejected out of hand need to be encouraged a little and given some resources. With a little time they may come back you with something that changes your opinion.

There are surely multiple factors. One of them is how the two sides approached a common problem differently. The common problem was the stagnation of movement (i.e. trench warfare). No side was able to effectively break the others side line.

The British approached that by building tanks. The Germans by developing special infantry tactics. They introduced "Storm Battalions" consisting of special trained infantry men ("storm troopers") and using mixed formations and weapons like, grenade launchers, flame throwers, light machine guns.

Each storm trooper was trained on all those weapons plus on enemy weapons. Tactics differed from the normal infantry. This was to wait for an artillery barrage and then storming the enemy lines in waves. Instead, storm battalions tried to reconnoiter weak spots in enemy lines and focus the attacks there to create a local overweight in fire power. Goal was not to take and hold trenches but to create a breakthrough.

The German armies back to to the Prussian army always had the focus on the "Auftragstaktik", roughly translated to "mission-type tactics" versus the strong hierarchy in the British or French Army. Those "mission-type tactics" where especially and strongly applied to the storm troopers compared to the regular infantry. Basically they were given the goal of the mission and completely in charge on how to achieve it. It actually included allowed subordination if the situation demanded it. This also supported the tactics of a specialized breakthrough force.

On the defense side the Germans focused on an asymmetric approach. Means, the solution for the stalled front lines where the storm battalions but the defense against the British solution for that problem ("tanks") was to use special weapons. This lead to the first development of anti tank weapons like the TAK 1918 or the "tank rifle".

All in all this was basically the foundation of what the Wehrmacht later further developed to their doctrines of "combined warfare" or "war of movement" in WW2. Or the approach to use tanks as breakthrough attack weapons and use anti tank cannons for defense against enemy tanks. They did not plan tank to tank warfare initially.

Thus the German high command did not focus on tanks by intention. They were convinced that introducing a flexible and powerful infantry force with focus on breakthrough tactics was better than using slow and inflexible machines that where just embedded into the same existing structure.

Like said, this was possibly only one reason. Another reason later in war was the lack of raw materials and currency. Germany was running out of steel and money. E.g. they had the slogan "gold for iron". German women should trade in all their gold jewelry for iron jewelry. So, when they traded in a golden ring they received an iron ring with the engravings "I gave gold for iron".