differential instrumentation amplifier in LTspice not working
Without the negative supply, the lower op-amp (U2) circuit can't work correctly because it is driven with a signal of +2 volts at its non-inverting input but, there is an overriding +3 volts forcing its way from the upper op-amp (U1) circuit via R1 to its inverting terminal. The net effect is that U2 naturally will want to produce a negative output voltage.
Using a negative supply instead of 0 volts rectifies this.
You can check this for yourself by looking at U2's output voltage relative to ground rather than trying to figure out things from the ambiguous (and non-informative) differential output voltage.