Shouldn't use two extreme gears?

I purchased a new Mountain bike a month ago and noticed after a week or so the gears were starting to slip, this was expected because of stretch in cables and wear in etc so I took it in for a tune up at the place of purchase and when I got it back the gears were still slipping in places.

I then took the bike to a local mechanic and he said that I shouldn’t be using the gears on the high extremes ie the two smallest cogs at the back because of the angle of the chain. I will admit I am no expert but in all my life I have not heard this, is this true?

Thanks

Thanks to all that answered! and to add to my question to clarify some points, i have 3 chain rings on the front and the slipping sensation is more like a clunk from the front crank when i put pressure on the pedals, its not a constant noise. this happens on a flat surface so its impossible to use this gearing on an incline.
It only happens when i have the chain on the small front ring and either of the two smallest back cogs.

I also get a ‘ghost’ gear shift when i use the middle front chain ring and either of the two smallest back cogs.

There seems to be polarising opinions about cross chaining which i will look into but either way i think i should be able to use all my gears if i want too. yes?