Why? Because it's just assumed to work in this way. It's only a widely used simplified way to think a diode, which in reality is more complex. As soon as any external circuit (see NOTE1) tries to lift the voltage over the diode higher than 0.7 volts, the diode sinks more current, so much more that the voltage stays at 0.7 V. That's for silicon PN diodes. Other diodes need other assumptions.
A real diode obeys a non-linear approximately logarithmic equation between the current and voltage, the "sink so much current that the voltage doesn't get higher than 0.7 V" is used in practical applications only because it often gives an approximated, but realistic view how a circuit works. For example I have hundreds of times searched faults in electronic devices and checked with a multimeter or an oscilloscope do the approximately 0.7 V voltages over the diodes exist right.
The model is useless when one should take into the account the temperature, capacitive behaviour, breakdown effects (Zener, avalanche), light and, of course, the exact real relation (= a smooth curve) between the voltage over the diode and the current through it. For example a logarithmic amplifier is based on that smooth curve.
NOTE1: the voltage source + the voltage divider. Mathematical solution is possible for example by using the Thevenin equivalent of the external circuit. Harmfully the equations must generally be solved iteratively or graphically because the common logarithmic current vs voltage equation for diodes is unfriendly for algebraic methods.
