Diodes shall never be put in parallel, unless they are in the same package. (More or less true) :
From a thermal perspective: Having both of them in the same package guarantee the differents junctions are at the same temperature. The risk of unbalanced current, is still present, but every rise in temperature of one diode will impact other one. Which make a thermal runaway of one diode less likely.
From a current perspective: Whit that said, you shall never put diodes in parallel to increase the max current. Max current shall still be less that the individual maximum current of one diode. Because even in the same package diode can have different forward voltage, meaning an unequal current spread.
If the diodes are not in the same package : The false theory, is that the current will be spread accros the two diodes.
In fact what will happen is that the diode whith the lesser forward voltage with let pass more current. Provoking a rise in temperature, this rise in temperature cause the forward voltage to decrease even more due to the negative thermal coefficient of diode junctions. This is thermal runaway, where the diode will be destroyed due do this positive feedback loop.
This is explained partly in the following document : AN4381 Application note