a lighter shade of the background color ie a red apple's highlight would ba a lighter shade of red

I don't know if I can answer this question comprehensivly here but I can give you a brief explanation of lights/ darks/ and colour
The light source will determine the colour of the highlights but so will the local colour of the object itself, as will reflected light
The reason your art teacher said not to use white, is that most people starting out painting turn to white as the only way to lighten a colour, they also think that the lightest area in a painting must be white - True white really does not exist - as any white object will reflect the colours around it. Try setting up a still life of all white objects - you will soon see there are many shades of white. Next get a piece of white paper and cut a small little hole in the paper, close one eye and look through the hole at the still life- scan around the still life- you will be surprised and how dark this all white still life is., if you hold the white piece of paper up and compare the white paper to the lightest area in the still life - you maybe surprised to see that the white paper is by far the lightest thing, and even if you take pure white paint and put a dab of it on your white paper it will probably read as much lighter than the paper - white paint is extremely bright, and if used straight out of the tube it can look stark and out of place in a painting, Many beginners think highlight equals white or if they are painting a white object they go straight for the white paint - it looks bad.
Another rule in obsevational painting is if the light souce is warm (artifical lighting or very low morning/evening light) than the highlights are warm and the shadows are cool., If the light source is cool -(day light ) than the shadows are warm.
When painting a green or red object try using yellow to lighten the colour, white will only create a tint and can make things look flat. You can also use pure colour to decribe highlights, like there are many shade of blue - prussian blue is really dark - cerulean blue is much lighter - using pure colour with no white creates a very vibrant effect. It's all about personal choice, if u use white to lighten everything it will give you one effect if you use pure colour it will give another.
There is no set rule to what colour highlights are - it will depend on 1.Light source 2. Colour of object
3. Possible reflected light source
HAVE FUN GOOD LUCK

Hey YES there are rules in art, and until you know what they are you don't know when you can break them and why.
I would suggest that the best explanation of how to highlight your art work if by an artist named Lillydahl. she has a DVD on light and Shadow you can see on line at www.newcenturytv.com. (click on the artist section.)
In this 2 hour instruction she explains warm and cool lights, and depending on the indoor or outdoor lighting of your subject, and the reflective light from the sky and surrounding areas.,
The reason you don't do white is because it would draw your eye away from the center of interest or focal point of the painting. Warm light cool Shadow is a good rule, but the highlight may be any lighter value, depending on weather you are doing a colorist painting or tonal painting. The best explanation I have ever seen on this subject and lighting in general for artwork is on her DVD.