(pre-trained) python package for semantic word similarity
The spaCy Python package might work for you.  It allows you to easily "install" large pre-trained language models, and it provides a nice high-level interface for comparing word vectors.

To install spaCy:

pip install spacy

Then you need to download a language model.  I believe these models are trained on Common Crawl, which is a massive dataset.  You should choose one of the medium or large models, because the small models do not ship with word vectors.

python -m spacy download en_core_web_md

Using spacy models to compute word similarity is a breeze:

import spacy

# load the language model
nlp = spacy.load('en_core_web_md')

word1 = 'cat'
word2 = 'dog'

# convert the strings to spaCy Token objects
token1 = nlp(word1)[0]
token2 = nlp(word2)[0]

# compute word similarity
token1.similarity(token2)  # returns 0.80168


Here's an example that's more similar to the one in your question:

import spacy

nlp = spacy.load('en_core_web_md')
token = lambda word: nlp(word)[0]  # shortcut to convert string to spacy.Token
score_words = lambda w1, w2: token(w1).similarity(token(w2))

score_words("pilot", "airplane")      # 0.5998
score_words("student", "university")  # 0.7238
score_words("cat", "dog")             # 0.8017
score_words("cat", "airplane")        # 0.2654
score_words("student", "apple")       # 0.0928