Boxed hair colour is a professional stylist's worst nightmare. Hairdressers work with dye every day at the salon and boxed dyes simply can't measure up to the quality and results of the professional colours they use on their clients. It's not simply a matter of stylists trying to create a stigma surrounding boxed dye because it potentially loses them customers. They hate it because it simply doesn't work properly and is a compromise on quality for several reasons.
One size fits all mentality
Boxed colour is sold on the principle that one size fits all, but this is never the case. If you were to read the back of a box of black hair dye from the drug store, you'd assume from what it tells you that you can apply it to your hair and no matter whether your hair is a light blonde or a dark brown, the end result will be black. What it doesn't tell you however, is that you can't simply apply it to any shade of hair and expect the results it shows.
Hair is not a solid colour. When you look at someone's hair, what you are seeing is the combination of several different tones that combine to form the actual colour you see. In the case of blonde hair, there is significantly less red pigment present compared to shades of brown. If you were to apply a black boxed dye to blonde hair like this, you're more than likely to end up with a shade of unnatural dark blue because the boxed dye doesn't contain enough red pigment to form the appropriate colour when applied to hair that is devoid of its own red pigment.
Light hair that is coloured in the salon is generally filled first if it's being dyed darker. This means the stylist pre-colours it to add certain tones back in so that the final colour will be dye correctly. Boxed dyes can't do this, nor do they usually specify that it has to be done, because they are a one size fits all product whilst hair varies dramatically between different people.
Lack of control
When you use a boxed colour, you have no choice in the volume of peroxide used. The peroxide that is mixed with a colour acts as the developer and lightening agent, and is a crucial part of the whole dyeing process. Specific volumes of peroxide are used depending on individual needs, and the colour change that is to be achieved.
Boxed dyes in blonde shades may contain 30 vol peroxide, and whilst this is necessary to achieve the lift, it causes issues when the hair doesn't need this much lift. There's no reason you should be applying colour containing 30 vol developer to hair that is already blonde, but if you were to apply a boxed blonde dye, that's what you'd be getting. Whilst platinum could have been achieved with much more care in the salon, your hair is put through overkill in the case of the boxed dye, and the risk of damage is also increased substantially.
Boxed dyes generally include some form of bottle applicator. The simple truth is that hair dye is best applied from a bowl by brush, and this is not included with a boxed dye. The bottle applicator that is included, is practically useless for any form of precision, and there's no way you can hope to apply it to your regrowth without banding the colour over hair that has previously been dyed, increasing the risk of damage and creating unexpected results.
Salon dyes are used by the professionals because they're better. In much the same way that a professional painter will have higher quality paints available to them and know what would work best for your house, a hairdresser has higher quality dyes and wouldn't dream of using box dyes. They treat your hair as an individual because it is, and they use higher quality colour because it's a reflection of their passion for the job and gives the best results.