That doesn't come close to being true. Compare the Cambridge dictionary's "common definition":
> [summer] the season of the year between spring and autumn when the weather is warmest, lasting from June to September north of the equator and from December to March south of the equator
Wikipedia:
> Summer is the hottest of the four temperate seasons, occurring after spring and before autumn. At or centred on the summer solstice, the earliest sunrise and latest sunset occurs, daylight hours are longest and dark hours are shortest, with day length decreasing as the season progresses after the solstice. The date of the beginning of summer varies according to climate, tradition, and culture.
> From an astronomical view, the equinoxes and solstices would be the middle of the respective seasons, but sometimes astronomical summer is defined as starting at the solstice, the time of maximal insolation, often identified with the 21st day of June or December. By solar reckoning, summer instead starts on May Day and the summer solstice is Midsummer.