Why should a solar battery have twice the capacity in kWh as the inverter’s rated power in kW?

First: Technical reasons
If the inverter has a higher rated power than the solar battery, the battery may not be able to absorb all the available energy. Consider a battery that is only 10% charged: if a large inverter then operates at full power, harmonic oscillations can occur and place additional stress on the battery.

Second: Practical use
The solar battery should not only be useful on sunny summer days, but also across longer periods such as a rainy week or during spring and autumn. A larger battery can help cover more electricity consumption with solar energy.

Conclusion
A 2:1 ratio—a solar battery with twice the capacity in kWh as the inverter’s rated power in kW—has proved effective in practice. A 1:1 ratio is often selected for cost reasons and can also be suitable. As a general design principle, the battery should not be undersized relative to the inverter if efficiency and battery service life are to be maximised.