Is it true that English has the most words of any language?
This question is practically impossible to answer, for the reasons explained in the answer to How many words are there in the English language? However, it seems quite probable that English has more words than most comparable world languages.
The reason for this is historical. English was originally a Germanic language, related to Dutch and German, and it shares much of its grammar and basic vocabulary with those languages. However, after the Norman Conquest in 1066 it was hugely influenced by Norman French, which became the language of the ruling class for a considerable period, and by Latin, which was the language of scholarship and of the Church. Very large numbers of French and Latin words entered the language. Consequently, English has a much larger vocabulary than either the Germanic languages or the members of the Romance language family to which French belongs.
English is also very ready to accommodate foreign words, and as it has become an international language, it has absorbed vocabulary from a large number of other sources. This does, of course, assume that you ignore 'agglutinative' languages such as Finnish, in which words can be stuck together in long strings of indefinite length, and which therefore have an almost infinite number of 'words'.