Why is graphite brittle?
Hardness and brittleness are not contradictory properties. There are plenty of substances that are both hard and brittle (cast iron is a good example, glass is another).

And "strength" is different as well. It depends on context. Tensile strength is not necessarily related to ability to survive a blow: some compounds with high tensile strength (which basically means the compounds resist being stretched) are incredibly fragile (or brittle if you prefer that term). Some compounds with low tensile strength are very hard to break (nylon rope, for example).

Part of the problem is that many of the properties of materials are based on the structural properties of the bulk material not the idealised properties of the chemical bonds making up the material. Some metals, for example, are tough (not brittle) and are hard to break but this property arises because defects in the crystal structure can move around absorbing external stress. Brittleness is often caused because no such mechanism exists and, once a surface bond breaks, the stress on the next bond gets worse, releasing energy and propagating a crack, tearing the material apart. Glass often has many small surface cracks which, under tension, concentrate stress making them brittle and subject to falling apart. But very pure, carefully grown glass fibres can be nearly crack-free making them much stronger under the same stress. In short to explain brittleness, toughness or strength, you need to know the macroscopic makeup of the bulk material not just the chemical composition.

So it is with graphite. There is no easy mechanism in a single graphite crystal to dissipate stress if a bond breaks, so it will tend to be brittle. But most samples of graphite are not single crystals: in most cases they will consist of a bunch of small units with the layers oriented in different directions. So bulk graphite isn't just brittle but also soft as some orientations will slide easily around. And it is hard to even talk about bulk graphene because by definition it is a single layer or a very thin bundle of layers. When people say graphene is strong they usually mean that it has high tensile strength along the plane of the layers. This doesn't mean it isn't either brittle or hard and even if it were in some orientations, it probably would not be in others.