Your trainer is not an idiot but they aren’t giving you the explanation that you are paying for.
Running will burn calories, lots of them. If you take in less calories than you expend then over time you will lose WEIGHT. That weight will consist of both fat and muscle.
Our bodies are also exceptional at adapting to different situations regarding workload and diet. Your fitness will increase, meaning basically that it becomes easier for you to complete the run. This efficiency results in a saving of calories.
As you get fitter, you need to run further to get the result that you want. The moment that you get bored or disillusioned and stop the running, your new body will continue to demand the same input and will begin to store it. Your body does not know that you are sick of running so it stores energy expecting to need it. If you stop running, cut your calories immediately.
On the other hand, if you train with weights in the correct way, you will build extra muscle and you will gain WEIGHT. This weight will consist almost entirely of muscle. The additional muscle has energy needs and will immediately lift your metabolic rate 24 hours a day. Assuming that your diet is appropriate, your energy needs will exceed the input and you will lose fat at the same time that you are building muscle. Whether you lose or gain weight depends on the rate of muscle growth to fat usage.
That is basically what your trainer may have been trying to tell you. It certainly should be.
You’ll notice that I said “if you train with weights in the correct way” above. That means that you can do it wrong and many people do.
To get the result that I have outlined, you need to train hard. You need to train like you want to be muscular and strong even if you don’t want those things. The beauty of this is that you won’t get muscular and strong by mistake and you certainly won’t get there quickly. As soon as you have altered your body composition to look how you want it to look, you can back off the training to a maintenance level and stay that way for ever.
In relation to the statement that the only way to lose bodyfat is through diet, he is pretty much right in my opinion. There are other ways to lose bodyfat but the body adapts and they lose their effectiveness. Those other ways are also useless unless intake is appropriate.
It is also much easier to lose 500 calories out of a diet than it is to add 500 calories of exercise. A calorie is quite a lot of energy.
My advice would be to tell your trainer that you are interested in why he gets you to do things. Try to start a conversation on the subjects and see what you can learn so that you develop the skills to work it out for yourself. If he refuses to give you explanations, then he is an idiot and you can fire him. 😆