The basis of Trump’s claim is that mathematics and statistics show a number of anomalous results happening in this election which, while not evidence of fraud, are nonetheless red flags of possible electoral fraud, which gives weight to the claims of thousands of witnesses that have produced written testimony alleging widespread illegal or non-compliant electoral activity (which I will call traditional voter / electoral fraud) bringing into question the integrity or accuracy of the election result.
A lot of the "allegations" etc etc can be seen sites like American Thinker. I'm not suggesting they're all valid but they need to be tested in a court of law not in the opinion of the MSM, which, as you have noted, the MSM in the US is most definitely left-wing and are heavily in bed with the Democrats, which IMO, is not healthy for a vibrant democracy.
In the first Presidential debate, Chris Wallace asked Biden if he would wait until the vote was certified before he claimed the election – Biden said “Yes”. But he didn’t wait, which is extremely disappointing as this election is very close, as you are looking at a hundred odd thousand votes in half a dozen states that could swing it back. Of course, we can go back to 2000 when Al Gore claimed he'd won (supported by the media again then) and then nearly 40 odd days later conceded with the SCOTUS decision on Florida meant Bush won (we could go on and on re 2000 but that would be a distraction).
Trump’s language is very abrasive for sure but his claims / suspicions of electoral fraud deserve to be taken seriously. Yes they need to be fully substantiated and rigorously tested and we will know more about the strength of his case(s) after it has been filed and evidence presented in the next few weeks. Until then claims his case is baseless is itself baseless. Moreover, given the tight timeframes and massive effort required to pull a case like this together the notion that everything would be laid out on day one is nonsense. The basis of his claim is clear, how well it can be substantiated is unclear. It will also be the SCOTUS that will decide this, forget the other courts, they're just window dressing to the end game.
Indeed Biden was being advised by Hillary Clinton not to concede in the event he lost before he had pursued his legal options. What is good for the goose is good for the gander. And if you want to assume the mantle of Leader of the Free World a good starting point is proof you won a free and fair election.
Whichever way Trump’s litigation goes it has highlighted that the US voting system is seriously broken and in chronic need of reform. For a country that routinely self proclaims to be the “world’s greatest democracy” its voting system is an embarrassment and disgrace and no amount of media denial can hide the fact.
At least then we can have a friendly, reasoned discussion about this without the rancour that has infected the US political scene.