Scaling is the process of cleaning up of your teeth of the depositions that has occurred over time.
It is a wrong perception that scaling makes your teeth weak or it removes a layer of your teeth.
Scaling is the treatment for periodontitis, it is a prophylactic treatment. It does not removes the tooth layer but the plaque and calculus from your tooth.
During scaling, there may be mild bleeding, it is not due to any harm to your oral health but due to the infection in your gums and bones.
You may have slight sensitivity after the scaling procedure, it is because earlier you were carrying chunks of calculus over your teeth and after it is removed your teeth is exposed to the oral fluids again. Like you feel sensitive to the area when a bandage has been removed after a long period.
Scaling is recommended every 6months, and thus any discomfort you feel that time is just for a day or two and nothing to worry about.