There are classical composers today. Most college music degree programs include degrees in composition. Though there are a couple reasons why it may seem like there aren't modern classical composers.
First, there are a couple definitions of classical music. One is an overarching, general definition that has basically come to mean music of the past, especially within the time of composers like Beethoven, Mozart, Chopin, Brahms, Bach, etc. There is a much more specific definition of classical music that refers to a specific musical era (approx. 1730 (the death of Bach) - 1820 (Beethoven)). This definition fits in a list of musical eras based on year and style changes: Medieval, Renaissance, Baroque, Classical, Romantic, Modern, 21st Century (the last two have a myriad of subcategories).
Second, modern classical composers use a wide range of styles to compose. Some work within the styles of the various eras but those are classified either in a modern category or considered neo-classical (or neo-baroque, neo-romantic, etc.). Others work with atonal or experimental styles. One of the characterizations of current "classical" music that differentiates it from other eras is that almost anything goes.
Third, historical classical music was the popular music of the time, while today we make a distinction between popular music and what we think of as a classical style. You would never hear a modern classical composer on a top 40 radio station so it sounds very different than solo piano repertoire or a large orchestral work.
Music of every era is going to sound a little different than the others while also including some similarities.
Here is a very short list of some 21st Century piano composers within my personal experience (Google will offer more):
Yiruma (more popular)
Jon Schmidt (of Piano Guys more popular)
Paul Paccione (my theory professor)
James Caldwell (my theory professor)
Hong-Da Chin (WIU music professor)