This is not necessarily true. Read this article by BOB, KONR.
"Let’s start with a simple example: a dummy load. A dummy load is basically a resistor that replaces the antenna so we can test transmitters without actually radiating a signal. For ham radio use, a dummy load will be a 50 Ω resistor, consistent with the fact that most ham radio systems operate at 50 ohms. A good dummy load provides an excellent impedance match at all frequencies of interest and it is not resonant. I say its not resonant because the load looks like 50 Ω for all frequencies (within a specified range). Its antenna efficiency is zero, because it does not radiate any of the power. So here we have a great example of a low SWR but no resonance and no radiated power.
Now let’s look at the classic center-fed half-wave dipole (1/4 wave per side) in free space. At the resonant frequency, the antenna has a characteristic impedance of 73 Ω, purely resistive. The SWR can be calculated by taking the ratio of the impedance to 50 ohms, giving SWR = 73/50 = 1.5. (By the way, for impedances less than 50 ohms, the SWR is calculated using SWR = 50/R.) Dipole antennas generally work well, so the antenna efficiency will be high and depends on the actual construction of the antenna. Note that the SWR is not equal to 1 at resonance, it is a bit higher. However, an SWR of 1.5 does represent a good match and is normally considered just fine.
Now let’s take a look at an antenna that is no where near 50 Ω at resonance, the half-wave folded dipole antenna. This antenna has an impedance of about 280 Ω at its resonant frequency. If we connect this antenna to a 50 Ω transmitter, the SWR is 280/50 = 5.6. So here is an example of a resonant antenna that has a high SWR. At the resonant frequency, this antenna will radiate efficiently but will present a difficult impedance match to a 50 Ω transmitter, which will struggle to deliver power from the transmitter into the antenna. While we might choose to accept this high SWR, a more practical approach is to add a matching network to produce a 50 Ω impedance match.
Many of the antennas we use are designed to be close to 50 ohm (SWR = 1) when they are resonant. For these cases, SWR is a good indicator that the antenna is resonant, which is why most hams associate low SWR with resonance. Low SWR does not tell us anything about how well the antenna is working (antenna efficiency). A dummy load has excellent SWR but fails to radiate. Some antennas are like that, too."
73, Bob K0NR
