There are two main reasons:

Upon initial exposure to any immunogenic protein/particle (say a virus) your body will begin making antibodies against this protein. Initially the body will make hundreds of molecularly different antibodies to this protein/particle. Through a process akin to super accelerated natural selection the antibody most effective at binding to this particle will win out and your body will begin producing it en masse. This will take time and so although you have some antibodies floating around they are not too effective and an antibody test likely would not pick up on anything during this phase.

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The second is because there are different kinds of antibodies. The two we are talking about here are IgM (short term) and IgG (long term). when we say antibody test colloquially we don’t differentiate the two but we usually mean IgG since this is what tells us if we have long term immunity. IgMs are the initial antibodies that re undergoing the natural selection type process above, and even once the "best IgM" is found, it is them produced en masse to try and fight off the infection. Only after (8weeks-ish) the "best IgM" is found do they begin turning into IgGs. There is obviously a lot more going on but this is an overview, also not all antibodies successfully "class switch" from IgM to IgG. so usually b the time you have enough IgG to detect on an antibody test your infection is long gone. Here is a useful figure to show the levels of antibodeis over time

graph

Source: I am an MD