The arguments against this are that it doesn't match what we currently see in the evolution of our universe.
The current best "concordance model" in cosmology (a.k.a. the Lambda-CDM model) is based on an expansion from an initially small, hot state, following the Friedmann equations. The best-fitting parameters of this model (using observations of the cosmic microwave background, the distances and redshifts of Type Ia supernovae, the primordial abundances of deuterium and helium, the motions of objects in galaxies and clusters of galaxies, the large scale structure in the universe, and others) suggest that the universe is spatially flat (Euclidean) and is now expanding at an accelerating rate.
In the context of the Lambda-CDM model, there is no observational evidence that would support the notion that the universal expansion will slow down and reverse.
There are of course problems with the Lambda-CDM model - the most important of which, in my view, is growing evidence that the universe is not homogeneous on quite large scales (an assumption baked in to the model) and this might lead to problems in interpreting the observations. No doubt you could invent other models, or extensions to the Lambda-CDM model that would allow the various properties of dark matter and energy to change in time such that the universe did collapse.