The LBS examined it and the new chain wasn't fitting the shape of the old casset.
the cassette had worn away to fit the old chain, and the new chain wouldnt fit on most of the teeth.
most likely your cassette.
Thats just like saying everytime you get new tubes you have to get new tires too...
Check the length of the chain first. I just put a new chain on my bike and I had to remove 7 links for it to fit correctly. If the cassette is worn then the obvious will present itself.
Obviously you need to shorten a new chain before installing. Maybe I should not have assumed the OP did that. And, no it is not just like saying you need new tubes with new tires. That is a dumb comparison. All I am saying is if you wait too long to replace a chain, you will be replacing the cassette with it.
From my experience, I had a new chain skip with a 2000 mi cassette (road bike) and there were no obvious signs of wear presented to me. The fact that the OP's bike looks cheap suggested to me that the cassette is probably cheap and worn out too.
Either way it doesn't matter to me. I threw what I thought out there and you disagree.