Arguments in favour of spelling reform
Because of historical reasons, spelling and pronunciation no longer match, and spelling needs to be adapted to take account of the changes that have taken place.
As an example of the problem the pronunciation of some words vary with context. Examples include: read, wind and bow.
The truth is that spellings do change - just very slowly.
Arguments against spelling reform
The majority of the (adult) population has consistently been against the idea. Presumably because they do not want to learn a new way to spell.
There is no single correct dialect within any one English speaking country - much less any accepted "correct" international form of the language. Would the citizens of the USA accept a spelling system based on an English pronunciation? Would the Scots? Would the Australians accept a spelling system based on American pronunciation? The advantage of the present system is that it is acceptable to all, the alternative would be to have a multiplicity of different spelling systems for each country.
And how would a hypothetical new spelling system be introduced? Most other languages have national or or international regulatory bodies which are charged with setting standards and enforcing (if they can) some form of prescriptive grammar. No such body exists for the English language, and creating one and giving it authority over the international language would probably be a larger task the the spelling reform itself.
The existing spelling system gives some clue to the origin of the word. This is surprisingly helpful when learning some foreign languages.
There is an immense literature, both printed and on the web, which uses the existing system. Spelling reform would put the former beyond the understanding of all but experts (unless it were "translated") and would involve major inconvenience in updating the latter.
English has over twenty vowel sounds which must be expressed using five letters - AEIOU. Any reformed spelling system would either need to introduce new letters or diacritic marks to indicate the sounds.