This statement shows a profound misunderstanding of how computational complexity works.
Yes, computer algorithms can output things that are not (intentionally) programmed into them.
There are two or three secret magic things which result in that happening:
The first is (effectively) random input. An algorithm may be attached to an input device (e.g. a sensory device, or text inputter aimed at most of all human Internet text expressions...) which sends the algorithm an effectively random sequence of input data.
The second is loops which can be designed to feedback a functional result of one piece of random input as input to the next processing round so that the first random data helps determine the direction/extent of algorithmic processing of a subsequent different random input. I say the feedback loop "helps" determine the further processing, because a third magic element, the conditional statement, branches the processing (in the loop) this way and that depending on this or that small detail of the (effectively random, remember) input or the (even more complex and completely unpredictable) combination of past and present inputs.
No programmer could possible keep up with the complexity of how this looping, conditional execution with random input sequences will go. No programmer can, in general, know where this kind of processing will end up, and with what result, nor even, can they predict if the program will keep looping or stop with a result.
Finite, simple algorithms, particularly with random input sequences (although those is not even strictly necessary) can generate arbitrary, unpredictable results. There is actual well-known math behind what I've tried to say in lay terms here.