The phenomenon you're describing is due to the interaction of light with the surface of your black t-shirt. While it's true that black objects generally absorb light rather than reflecting it, the behavior of light can be more complex depending on the specific materials involved.
When light from a flashlight strikes your black t-shirt, some of the light is indeed absorbed by the fabric. However, not all wavelengths of light are absorbed equally. The black color of the fabric arises from the fact that it absorbs light across a wide range of wavelengths, including those visible to our eyes. But there are still some wavelengths of light that the fabric does not absorb as effectively.
It's likely that the flashlight emits light at a range of wavelengths, and some of those wavelengths are not absorbed by the black fabric but instead get scattered or reflected. These scattered or reflected wavelengths can then reach your eyes, allowing you to see the light from the flashlight.
Additionally, the texture and composition of the fabric can also affect how light interacts with it. The surface of the fabric may have microscopic irregularities or fibers that scatter or reflect the light in various directions, further contributing to the visibility of the light.
In summary, while black objects absorb a significant amount of light, the specific properties of the material and the characteristics of the incident light can result in some light being scattered or reflected, making it possible for you to see the light from your flashlight on a black t-shirt.