The liner is just that a liner, it is not designed to support any weight. So when you fit your liner to an empty Brown bin, if you allow too much of the liner to extend over the lip of the bin then the liner now shortened, will not reach the bottom of the bin.
As you fill up your bin the waste does not fall to the bottom of the bin but instead it is supported by the suspended liner, which then stretches with the weight of the waste, and causes the liner to tear under the strain.
So when fitting your bin liner first open it between your thumbs, and using your two hands shake in the air to fully expand it.
Then allow the bag to rest on the bottom of the bin, and just leave the minimal amount of an overlap at the lip of the bin and it will not tear when weighed down with waste.