First we need to know what a programming language is. At its minimum, a programming language is something that is read by the computer and instructs it to perform certain operations. Many people would also expect a general purpose programming language to be Turing complete. However there could be situations where a domain-specific language isn't Turing complete but is still a useful programming language for that specific domain. Programming languages can be compiled or interpreted, and they could run on many platforms or just one specific one. Different needs require different programming languages. Clearly PHP is a programming language.
My definition of "real" programming language would be any programming language that has at least one practical usage in the real world. This is opposed to an esoteric programming language which typically has no practical usage. Since PHP is used widely to solve real problems it easily meets this requirement for being a real programming language, although it is arguably not a particularly beautiful language.
PHP is a pragmatic language. It was created out of a specific need to be able to quickly make web pages (the name originally stood for Personal Home Pages) and the language was extended as required. Since there was no theoretical background or strong design principles driving its creation (there isn't even a formal specification of the language) it is less clean than many other more modern languages. Features like correct handling of foreign characters / unicode characters are obviously added on afterwards and not cleanly integrated with the rest of the language. This untidiness and lack of theoretical rigour causes many people (especially academics) to dislike the language and this may be part of the reason why your teacher doesn't regard PHP as "real" language.
However PHP is good at what it was designed for and many sites use it, even very large sites like Facebook, Yahoo! and Wikipedia.
