Your trainer could be right and just might be concerned that for the amount of exercise you're doing that you may not be eating enough. It's pretty shocking how much we can actually eat! If you're eating a lot of non-processed fresh things then you will find it is quite a lot of food and I'm sure it feels like SO MUCH, but try to compare it to the nutritional value of the food you were eating before. It's pretty easy to consume a lot of empty calories when you're not paying attention.
For example, I need around 2,000 calories to maintain my weight as I'm a very active, 118 pound person. Seems like a lot (and it is a lot of food if you eat the right things) but when I stick to 1600-1800 I lose weight!
That said, the amount you're eating isn't too low or too high and you know you can lose weight on it. If you want to try what your trainer suggests, you may be pleasantly surprised. Otherwise you're doing fine
