The property management company refused to rent a house for me!

You should first confirm whether the purpose of the house recorded in the property certificate you are renting is "commercial and residential". If yes, the property has no right to refuse. If only "residence" is recorded, the property can prohibit you from using it.

The key is whether you change the use of the house at will, that is, about the so-called "from living to non-living", training is regarded as commercial use.