Low earth orbit is at a speed of 28,080 km/h. If you want to separate the two halves of your satelite at a significant angle from their starting trajectory, you

Low earth orbit is at a speed of 28,080 km/h. If you want to separate the two halves of your satelite at a significant angle from their starting trajectory, you have to provide a lot of impulse perpendicular to the direction of travel (or from a zero-orbital speed vertical launch at apogee, which would be weird). More impulse than an explosion could make, probably even if you built your satellite like a brick shithouse. Rockets conveniently spread the impulse out over a long period of time.