But that you have training for that.

其实你误解了training,它的确可以做名词。这里用的不是现在完成时,用的是现在时。have在这里做及物动词“有”。但是换个角度,如果你写But that you have been trained for that。句子没错,意思和以前不一样了。原本是“但是,你有这方面的培训呀!”改成现在完成时意思就是：“但是,你已经在这方便被培训过了呀!”意思上有小小差异!