Taking place in a sci-fi universe during a massive conflict. In this universe, however, robots are a major industry, so it would make sense that the government would specially create robots for this massive conflict. However, it is necessary to the story's plot that this does not happen and human soldiers are the main force.
So without looking too far into the conflict itself, what are some logical reasons why humans would be trained in this army instead of robots?
A lot of good answers here, but one thing to consider is the purpose of war itself. This is to inflict a sufficiently grave defeat upon the enemy as to completely demoralize him and motivate his surrender. I get that robots would be useful for a superior power to control a lesser one (cf USA and drones), but a war of robots against robots would be inconclusive. At some point, something important has to be at stake -- which can only be a human life.
If your story allow cloning. You can use the passion of Star Wars fans. Who would win between droids vs clones or what advantages clones oppose against droid are questions they love to debate. You can find online a lot of talks. Even on SE: Why Did the Empire Use Storm/Clone Troopers and not Droids?
For example this answer by HNL:
Droids lack certain qualities that most humans (even clones) possess: grasping the subtleties of situations, thinking on their feet and adapting. [...]
There are droids with advanced faculties, but they are likely to be expensive models -- not ones that you can mass produce in the millions and deploy into battle fields. [...]
[...]
Despite these advantages, however, combat droids suffered from several drawbacks. Most importantly, in order to create total obedience and foil any chance of rebellion, droid units were often crippled with extremely sub-par artificial intelligence.
What about cyborgs (50% human %50 robot), exo-skeletons or even mechas? The problem with drone or robot is that you need a connection to be controlled by humans or to let them communicate with each other. Any communication like this could be subject to hack like Man in the Middle or else. And I dont talk about bug. If each bot is controlled directly by the soldier inside it, you limit a ton of risk and you reduce the difference of force between full robot and basic soldier.
Make everyone in your universe agree that violating Asimov's 1st Law of Robotics is a very bad idea
Creating a strong artificial intelligence which ever considers killing a person a viable option is recipe for disaster. The risk of a violent AI uprising just becomes too high. Even more so if you hard-wire them to lethal weapon systems. Maybe something similar has already happened in the past, and everyone learned their lesson. Or maybe people are just smart enough to realize this danger on their own. Therefor everyone in your universe agrees that robots must be programmed with a generally agreed upon set of core ethic rules, with "Do not harm humans" as priority one (compare: Isaac Asimov's Laws of Robotics).
This makes strong AI unusable for military applications. Computers in the army will be limited to classic programming or weak AI incapable of reasoning beyond its specialized problem domain. That means armies will likely have a lot of computer assistance and employ automated systems for simple tasks (like they already do). Maybe you will even see fully autonomous weapon systems (which currently aren't that far into the future), but they would be too stupid to do anything except following simple, preprogrammed orders ("patrol between points A and point B and fire on every person who wears a uniform of country C"). That would make them easy to trick and incapable of reacting to unforeseen situations. So humans will still be required as the main decision makers.
I would say that cost is your biggest hurdle. Cost to build the one robot, cost to repair it, cost to keep fueled, maintained, updated with new software. Cost, cost, cost. There are of course costs associated with live soldiers, but your story should make it clear that robots are far costlier.
Also your character(s) could use the argument that live soldiers wouldn't make the mistakes that robots would make as they know right and wrong and can think creatively. This argument may not be sincere but that would be up to you.
Edit: Something else occurred to me. What if the reason is some event that happened in your stories past? What if there was a huge robot revolt that cost many lives, so now they make sure that robots are never used in warfare. Just a thought. Something like that is part of the backstory in Dune.
