im sorry about to hear that the trainer was a little old school when it comes to harnesses and small breeds. I do suggest you just ignore it and use the harness that you have although if she really see's it as a training issue there are other options available to you. I have friends that use font lead harnesses. they are safe for small breeds and many large breed owners have started using them also since they dont believe in pulling necks either. They look like this.
Front Lead No Pull Dog Harness Made in USA | eBay
they're basically harnesses with the ring in the front instead of the back. They do help when training loose leash walking since it prevents the dog from walking in front of you. I find a regular harness works fine for me but some dogs are bigger puller than others
Good luck in your training! i hope the rest of the classes get better.