Volcanoes are not, in any meaningful sense of the word, alive. Volcanoes are rocky structures formed by the ejection of molten rock through weak spots in the Earth's crust, according to Oregon State University. Apart from some of the gases they expel, they are primarily silicon-based, not carbon-based.
Life, as it is understood by humans, is exclusively built around carbon atoms. In order to be alive, according to Learningscience.org, an organic entity must theoretically be capable of reproducing offspring that resemble the parent more than others in the population. Even when a mature volcano spawns a second, younger volcano, it has not strictly reproduced through heredity.