While time dilation is a real phenomenon, its effects are not readily noticeable in our everyday lives because the differences in time scales and velocities involved are usually very small in ordinary circumstances.
Time dilation becomes more significant as the relative velocities approach the speed of light or when strong gravitational fields are present. In our daily experiences, the velocities we encounter are much lower compared to the speed of light, and the gravitational fields we encounter are not extremely intense. Therefore, the time dilation effects we observe in our everyday lives are negligible.
However, even though the effects are small, they are still present. For example, the Global Positioning System (GPS) navigation system relies on highly accurate timekeeping, and if the time dilation effects of both special and general relativity were not taken into account, GPS calculations would quickly become inaccurate by several kilometers.
Additionally, atomic clocks that are highly precise instruments are capable of measuring tiny differences in time due to relative motion or gravitational fields. These experiments have confirmed the predictions of time dilation made by the theory of relativity.
So, while time dilation does occur, its effects are usually only significant in extreme conditions involving high velocities, strong gravitational fields, or highly precise measurements. In our everyday lives, these effects are generally too small to be noticeable without specialized instruments or observations conducted under specific circumstances.