I assume you mean offense and by that I assume why is it illegal.
In the United States, 42 states dictate that a tread depth of 2/32's is the minimum allowable on a passenger car tire tread. That is 1/16ths of an inch to those who flunked fractions in elementary school. That is the approximate distance between the base of a new penny and Abraham Lincoln's head.
Consumer reports published an article in 2007 that their research indicated 4/32nds should be the minimum tread depth based upon braking and steering tests. That is the approximate distance between the base of a new quarter and George Washington's head. That is 1/8ths of an inch.
Tread is placed on tires to take water away from the tire and the road surface and increase the coefficient of friction (a measurement of traction) in inclement weather. Some tread patterns and tire materials are better than others in different situations which is why tire companies sell snow tires, rain tires, and all season tires. All tires are a combination of give and take on what is the best tread pattern, tire rubber compounds, construction, etc.
As the tire tread wears, this might increase traction in dry conditions which is why drag race cars often use "slicks" tires with no tread pattern, but these are useless if the roadway gets wet and no one can predict where and when that might happen on public roads. More tread reduces this potential for loss of traction significantly, but only if it is of sufficient depth and the research indicates that tires should be replaced when the tread depth is at least 2/32nds and preferably by 4/32nds.
When the tread gets low.
When your tires squeal at a low speed it can mean a number of things. The tread on your tires may be almost gone or you may have low tire pressure.
More than narrow tread tires.
Poorly inflated tyres and unbalanced wheels and tracking.
Minimum tread depth for all 4 tires is 2/32"
60% tread wear.
Many tires have tread wear indicator bars molded into the tread. When the tread is worn down to where you can see a solid bar of rubber across the width of the tread, it is time to replace the tire.
A good test is to take a penny and place it in the tread grove with the head of Lincoln facing down. If you can see the top of Lincoln's head you need new tires. If the tread is worn more on the inside or outside you need a front end alignment. If the tread is worn on the outer edges you are running the tires with too low air pressure. Worn in the center, too much air pressure. Of course dry rotted and cracked tires need replacing no matter the tread depth.
I assume you are referring to the tread. High grip will have a more aggressive tread design used in off-road conditions or in deep snow. They are called off-road tires or snow tires. The difference is in the tread design.
While it is good to use tires with the same tread and sizes, it is possible to use tires with different tread patterns, though you should be careful as the performance of the two tires may be different, causing your car to be unbalanced, endangering your passengers.
Because they have more tread.
Only aggressive tread new tires whine.