you need to start by understanding that you will never win an argument with your parents. your dad will not change his mind and your mum will not stop supporting him. right or wrong has nothing to do with this. it doesn't matter that you are right, you cannot win by arguing. you need to start by accepting that point.
I suggest two things:
1. you have a general conversation with your parents about how things change over time. back in the day, folks rode horses everywhere and now everyone has a car. once, child mortality was very high, now medical advances and vaccinations and better diet and so forth mean that child mortality is very low. once upon a time, space travel and moving pictures were just fantastical dreams, but today everyone watches Youtube videos of a remote controlled car on the planet Mars on their phone. once upon a time, America was a vast open prairie populated by a horse riding nomadic peace-loving people who lived in tents and cooked over an open fire; today, Minneapolis. stuff happens, and things change. observations of these changes are what's called history.
this does not have to have anything to do with running, and you will probably need to visit this topic more than once, so have lots of examples: black & white movies are now full colour with cgi and virtual actors instead of stuntmen going over waterfalls in a barrel. a machine in a coffee shop that plays 45 rpm records for 10c each has been replaced by digital music on an iPod with each customer having their own personal selection and private ear phones. keep having this conversation and make sure it doesn't lead directly to running or training. you could mention that science is the process of discovering these changes. try not to use the word progress.
eventually, after laying some ground work with the above, you make the subtle observation that the training that Olympic Champion Matt Centrowitz does is significantly different to the training that Roger Bannister did, that John Walker did or that Sebastian Coe did. no one trains like Emil Zátopek anymore, stuff happens, things change. just like there are no Indians anymore, no one does high knees anymore. you might also like to make the point that you train the athlete not the event, but I don't get the impression your dad is into such subtleties and he may not even understand what you're saying. but it remains true, you train the athlete, not the event. you are not him and have to do your training, not his.
2. buy him a book. if you've read Daniels, let him read that. or get him Running with the Buffaloes, or a book on Jim Ryun or indeed any half-decent biography of any middle-distance runner he admires. DO NOT present to him with a flourish as though it is some mind altering drug or something. just buy him a book, and give it to him as a gift, because you thought he might like to read it. wait some days for him to read it, or to have started reading it, then talk about it. talk about how the guys go for long runs, and do fartleks and tempos and stuff, and they run long intervals, and they do stuff that is tailored to each individual athlete and they don't seem to do very much of the stuff that he did, back in the day. try to let him do the work of joing up the dots here, so that when he "discovers" this amazing truth he is a clever and perceptive fellow to be admired for his clarity of vision and open-minded search for truth justice and the American way. or something.
cheers.