The data sheet for P89c51 - P2 pin High Level output current says :
VOH @ VCC = 4.5V and IOH = -30 microAmp.

The data sheet for DM74LS573 says for High Level Input current :
IOH = 20 microAmp ( and 9 such were being driven by the 89c52!)

Dear Raghunathan,

specified data are maximums and minimums! Means, there's a lot of headroom, so that the circuit CAN work:

IIH = 20 µA is, what manufacturer guarantees to be never exceeded over whole operation temperature range: So, at room temperature observed IIH can be much smaller.

And VOH of P2 at IOH = -30µA is guaranteed to be never exceeded over whole operation temperature range: So, at room temperature observed VOH can be much higher.

Also, keep in mind, that 74LS chips can work with VIH >= 2.0V. Your micro can deliver much more current at VOH = 2.4V than only -30µA, about 3...5 times more (depends on derivative).

All these points show, that your circuit CAN work. But it's not a good design practice to assume standard data. It's much better to work like a professional, and think about worst case conditions. By this you would at least use pull-up resistors at P2 pins. 4k7-array is a good choice, e.g.

How do I explain THAT to the guy ?

Tell him, that the circuit is not professionally designed. So, sometimes it works, sometimes it doesn't. Adding of pull-ups is mandatory.

Merry Christmas,

Kai