Subcarrier spacing in OFDM
There are many intepretation of OFDM to answer your question. One way I find intuitive is looking at the resolution of (Discrete) Fourier Transform.

By capturing a signal during time $T$, and by assuming periodicity outside $T$, DTFT is able to provide a frequency resolution $1/T$. Thus if you choose a subcarrier spacing $\Delta f$, you will want a frequency resolution at least $\Delta f$. As a consequence, signal must be captured at least $T = 1/\Delta f$.

One may argue that I capture then $T &gt; 1/\Delta f$. It is fine, but the extra capturing time may catch the next symbol and cause ISI. Assuming that in a good system design, e.g. with CP or zero guard time, so that ISI is avoided, the resolution of DTFT (and DFT/IFFT) $1/T &lt; \Delta f$. The issue here is that if $\Delta f$ is not a multiple of $1/T$, the output of IFFT will be at frequencies $k/T, k \in \mathbb{Z}$ outside the subcarrier positions and this output will be sinc-interpolation of data.

So, at the end the requirement is $\Delta f=k/T, k \in \mathbb{N_+}$ or $T=k/\Delta f$. For the sake of economy, we choose the smallest $T$ possible at $k=1$ yeilding the famous thumb rule "subcarrier spacing is reciprocal of the symbol period".